We study the Picard groups of connected linear algebraic groups and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these groups in order to construct various examples of pathological behavior for the cohomology of commutative linear algebraic groups over local and global function fields.
{"title":"Translation-invariant line bundles on linear algebraic groups","authors":"Zev Rosengarten","doi":"10.1090/jag/753","DOIUrl":"https://doi.org/10.1090/jag/753","url":null,"abstract":"We study the Picard groups of connected linear algebraic groups and especially the subgroup of translation-invariant line bundles. We prove that this subgroup is finite over every global function field. We also utilize our study of these groups in order to construct various examples of pathological behavior for the cohomology of commutative linear algebraic groups over local and global function fields.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41736229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we give a recipe for producing infinitely many nondivisible codimension 2 2 cycles on a product of two or more very general Abelian varieties. In the process, we introduce the notion of “field of definition” for cycles in the Chow group modulo (a power of) a prime. We show that for a quite general class of codimension 2 2 cycles, that we call “primitive cycles”, the field of definition is a ramified extension of the function field of a modular variety. This ramification allows us to use Nori’s isogeny method (modified by Totaro) to produce infinitely many nondivisible cycles. As an application, we prove the Chow group modulo a prime of a product of three or more very general elliptic curves is infinite, generalizing work of Schoen.
{"title":"Nondivisible cycles on products of very general Abelian varieties","authors":"H. A. Diaz","doi":"10.1090/jag/775","DOIUrl":"https://doi.org/10.1090/jag/775","url":null,"abstract":"In this paper, we give a recipe for producing infinitely many nondivisible codimension \u0000\u0000 \u0000 2\u0000 2\u0000 \u0000\u0000 cycles on a product of two or more very general Abelian varieties. In the process, we introduce the notion of “field of definition” for cycles in the Chow group modulo (a power of) a prime. We show that for a quite general class of codimension \u0000\u0000 \u0000 2\u0000 2\u0000 \u0000\u0000 cycles, that we call “primitive cycles”, the field of definition is a ramified extension of the function field of a modular variety. This ramification allows us to use Nori’s isogeny method (modified by Totaro) to produce infinitely many nondivisible cycles. As an application, we prove the Chow group modulo a prime of a product of three or more very general elliptic curves is infinite, generalizing work of Schoen.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49040785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.
我们证明了每一个拟对数正则对都只有杜波依斯奇点。请注意，我们的参数不受最小模型程序的约束。
{"title":"Quasi-log canonical pairs are Du Bois","authors":"O. Fujino, Haidong Liu","doi":"10.1090/jag/756","DOIUrl":"https://doi.org/10.1090/jag/756","url":null,"abstract":"We prove that every quasi-log canonical pair has only Du Bois singularities. Note that our arguments are free from the minimal model program.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46959908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We characterize K. Kato’s log regularity in terms of vanishing of (co)homology of the logarithmic cotangent complex.
我们用对数余切复数的（co）同调的消失来刻画K.Kato的对数正则性。
{"title":"Homological characterization of regularity in logarithmic algebraic geometry","authors":"J. Conde-Lago, J. Majadas","doi":"10.1090/jag/787","DOIUrl":"https://doi.org/10.1090/jag/787","url":null,"abstract":"We characterize K. Kato’s log regularity in terms of vanishing of (co)homology of the logarithmic cotangent complex.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42179311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fibered varieties over curves with low slope and sharp bounds in dimension three","authors":"Yong Hu, Tongde Zhang","doi":"10.1090/jag/739","DOIUrl":"https://doi.org/10.1090/jag/739","url":null,"abstract":"<p>In this paper, we first construct varieties of any dimension <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n greater-than 2\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">n>2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> fibered over curves with low slopes. These examples violate the conjectural slope inequality of Barja and Stoppino [Springer Proc. Math. Stat. 71 (2014), pp. 1–40].</p>\u0000\u0000<p>Led by their conjecture, we focus on finding the lowest possible slope when <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n equals 3\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">n=3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Based on a characteristic <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>></mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">p > 0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> method, we prove that the sharp lower bound of the slope of fibered <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"3\">\u0000 <mml:semantics>\u0000 <mml:mn>3</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-folds over curves is <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4 slash 3\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mn>4</mml:mn>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">4/3</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, and it occurs only when the general fiber is a <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis 1 comma 2 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(1, 2)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-surface. Otherwise, the sharp lower bound is <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semantics>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:annotation encodi","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43991984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of existence of Kähler–Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 22 that admit a faithful action of the multiplicative group C ∗ mathbb {C}^ast . We prove that, with the possible exception of two explicitly described cases, all such smooth Fano threefolds are Kähler–Einstein.
{"title":"Kähler–Einstein Fano threefolds of degree 22","authors":"I. Cheltsov, C. Shramov","doi":"10.1090/jag/812","DOIUrl":"https://doi.org/10.1090/jag/812","url":null,"abstract":"We study the problem of existence of Kähler–Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree \u0000\u0000 \u0000 22\u0000 22\u0000 \u0000\u0000 that admit a faithful action of the multiplicative group \u0000\u0000 \u0000 \u0000 \u0000 C\u0000 \u0000 ∗\u0000 \u0000 mathbb {C}^ast\u0000 \u0000\u0000. We prove that, with the possible exception of two explicitly described cases, all such smooth Fano threefolds are Kähler–Einstein.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42756039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On smooth varieties, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. In dimension three, we reduce it to the case when the boundary is the product of a canonical part and the maximal ideal to some power. We prove the reduced assertion when the log canonical threshold of the maximal ideal is either at most one-half or at least one.
{"title":"On equivalent conjectures for minimal log discrepancies on smooth threefolds","authors":"M. Kawakita","doi":"10.1090/jag/757","DOIUrl":"https://doi.org/10.1090/jag/757","url":null,"abstract":"On smooth varieties, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. In dimension three, we reduce it to the case when the boundary is the product of a canonical part and the maximal ideal to some power. We prove the reduced assertion when the log canonical threshold of the maximal ideal is either at most one-half or at least one.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45766995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove Bloch’s formula for 0-cycles on affine schemes over algebraically closed fields. We prove this formula also for projective schemes over algebraically closed fields which are regular in codimension one. Several applications, including Bloch’s formula for 0-cycles with modulus, are derived.
{"title":"𝐾-theory and 0-cycles on schemes","authors":"Rahul Gupta, A. Krishna","doi":"10.1090/jag/744","DOIUrl":"https://doi.org/10.1090/jag/744","url":null,"abstract":"We prove Bloch’s formula for 0-cycles on affine schemes over algebraically closed fields. We prove this formula also for projective schemes over algebraically closed fields which are regular in codimension one. Several applications, including Bloch’s formula for 0-cycles with modulus, are derived.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/jag/744","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48564794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Martin G. Gulbrandsen, L. H. Halle, K. Hulek, Ziyu Zhang
<p>Given a strict simple degeneration <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f colon upper X right-arrow upper C"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:<!-- : --></mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">→<!-- → --></mml:mo> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">f colon Xto C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> the first three authors previously constructed a degeneration <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript upper X slash upper C Superscript n Baseline right-arrow upper C"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>I</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>X</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msubsup> <mml:mo stretchy="false">→<!-- → --></mml:mo> <mml:mi>C</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">I^n_{X/C} to C</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the relative degree <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> Hilbert scheme of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="0"> <mml:semantics> <mml:mn>0</mml:mn> <mml:annotation encoding="application/x-tex">0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dimensional subschemes. In this paper we investigate the geometry of this degeneration, in particular when the fibre dimension of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f"> <mml:semantics> <mml:mi>f</mml:mi> <mml:annotation encoding="application/x-tex">f</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is at most <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2"> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding="application/x-tex">2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. In this case we show that <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper I Subscript upper X slash upper C Superscript n Baseline right-arrow upper C"> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>I</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>X</mml:mi>
给定一个严格的简单退化f:X→ 前三位作者先前构建了一个退化的I X/C n→ C I^n_｛X/C｝到0维子项的相对次数n的Hilbert格式的C。在本文中，我们研究了这种退化的几何结构，特别是当f的纤维尺寸至多为2 2时。在这种情况下，我们证明了I X/C n→ ｛X/C｝ to C是一个dlt模型。如果f:X，这甚至是一个很好的最小dlt模型→ C f 冒号X 到C具有此属性。我们计算了中心纤维（IX/Cn）0（I^n_{X/C}）_0的对偶复形，并将其与一般纤维的基本骨架联系起来。对于K3表面的II型退化，我们证明了堆叠I X/C n→ C｛mathcal I｝^n_｛X/C｝to C具有无退化的相对对数2-形式。最后，我们讨论了我们的堕落与永井建筑的关系。
{"title":"The geometry of degenerations of Hilbert schemes of points","authors":"Martin G. Gulbrandsen, L. H. Halle, K. Hulek, Ziyu Zhang","doi":"10.1090/jag/765","DOIUrl":"https://doi.org/10.1090/jag/765","url":null,"abstract":"<p>Given a strict simple degeneration <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon upper X right-arrow upper C\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo>:<!-- : --></mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:mi>C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">f colon Xto C</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> the first three authors previously constructed a degeneration <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I Subscript upper X slash upper C Superscript n Baseline right-arrow upper C\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msubsup>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msubsup>\u0000 <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\u0000 <mml:mi>C</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">I^n_{X/C} to C</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of the relative degree <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\">\u0000 <mml:semantics>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> Hilbert scheme of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"0\">\u0000 <mml:semantics>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-dimensional subschemes. In this paper we investigate the geometry of this degeneration, in particular when the fibre dimension of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\">\u0000 <mml:semantics>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">f</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is at most <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semantics>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. In this case we show that <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper I Subscript upper X slash upper C Superscript n Baseline right-arrow upper C\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msubsup>\u0000 <mml:mi>I</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>X</mml:mi>\u0000 ","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46900861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We compute the characteristic cycle of a rank one sheaf on a smooth surface over a perfect field of positive characteristic. We construct a canonical lifting on the cotangent bundle of Kato’s logarithmic characteristic cycle using ramification theory and prove the equality of the characteristic cycle and the canonical lifting. As corollaries, we obtain a computation of the singular support in terms of ramification theory and the Milnor formula for the canonical lifting.
{"title":"Characteristic cycle of a rank one sheaf and ramification theory","authors":"Yuri Yatagawa","doi":"10.1090/jag/758","DOIUrl":"https://doi.org/10.1090/jag/758","url":null,"abstract":"We compute the characteristic cycle of a rank one sheaf on a smooth surface over a perfect field of positive characteristic. We construct a canonical lifting on the cotangent bundle of Kato’s logarithmic characteristic cycle using ramification theory and prove the equality of the characteristic cycle and the canonical lifting. As corollaries, we obtain a computation of the singular support in terms of ramification theory and the Milnor formula for the canonical lifting.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2017-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43724040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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