Pub Date : 2013-04-01DOI: 10.1017/IS013001031JKT215
T. J. Peter
{"title":"Prime Ideals of Mixed Artin-Tate Motives","authors":"T. J. Peter","doi":"10.1017/IS013001031JKT215","DOIUrl":"https://doi.org/10.1017/IS013001031JKT215","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"35 1","pages":"331-349"},"PeriodicalIF":0.0,"publicationDate":"2013-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91335689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-02-01DOI: 10.1017/IS013001008JKT197
A. S. Sivatski
Let p be a prime, F a field of characteristic different from p. We prove triviality of the divided power operations on central simple cyclic algebras of exponent p.
设p为素数，F为不同于p的特征域。证明了指数为p的中心简单循环代数的分幂运算的平凡性。
{"title":"Central simple algebras of prime exponent and divided power operations","authors":"A. S. Sivatski","doi":"10.1017/IS013001008JKT197","DOIUrl":"https://doi.org/10.1017/IS013001008JKT197","url":null,"abstract":"Let p be a prime, F a field of characteristic different from p. We prove triviality of the divided power operations on central simple cyclic algebras of exponent p.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"113-123"},"PeriodicalIF":0.0,"publicationDate":"2013-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS013001008JKT197","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56667438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2013-02-01DOI: 10.1017/IS012003019JKT187
C. Sherman
We establish a presentation for K 1 of any small exact category P , based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K 1 ( P ) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”
{"title":"K 1 of Exact Categories by Mirror Image Sequences","authors":"C. Sherman","doi":"10.1017/IS012003019JKT187","DOIUrl":"https://doi.org/10.1017/IS012003019JKT187","url":null,"abstract":"We establish a presentation for K 1 of any small exact category P , based on the notion of “mirror image sequence,” originally introduced by Grayson in 1979; as part of the proof, we show that every element of K 1 ( P ) arises from a mirror image sequence. This provides an alternative to Nenashev's presentation in terms of “double short exact sequences.”","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"155-181"},"PeriodicalIF":0.0,"publicationDate":"2013-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012003019JKT187","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Nanodiamond holds great interest in a variety of optical applications, the properties being correlated with surface modification, and the presence of both impurities and defects (contained either on their surface or within the crystal structure). Undecyl-nanodiamond produced by attachment of 1-undecene onto the nanodiamond surface could be a good candidate as a luminescent marker in the future; therefore, understanding of its optical properties is essential. In this work, the optical properties of the acid-purified nanodiamond and undecyl-nanodiamond were characterised using surface enhanced Raman spectroscopy (SERS) and photoluminescence spectroscopy. The results demonstrate that the characteristic diamond Raman signal at 1330 cm -1 was still observed after chemical surface modification, while the signal at ~1600 cm -1 (attributed to graphite bands) disappeared after the modification. Broad photoluminescence emission is detected in the range 1.5-2.5 eV (500-800 nm), as typically found for isolated nanodiamond; these emission bands became narrower with attachment of 1-undecene as compared to the sample without surface functionalisation. The observed emission could be related to structural disorder on the nanodiamond surface. The temperature dependence of the intensity, peak position and band widths of each sample has been characterised.
纳米金刚石在各种光学应用中有着很大的兴趣，其性质与表面修饰以及杂质和缺陷(包含在其表面或晶体结构内)的存在有关。由1-十一烯附着在纳米金刚石表面制备的十一烷基纳米金刚石是一种很好的发光标记材料;因此，了解其光学性质是必不可少的。本文采用表面增强拉曼光谱(SERS)和光致发光光谱对酸纯化纳米金刚石和十一烷基纳米金刚石的光学性质进行了表征。结果表明，化学表面修饰后1330 cm -1处仍有金刚石特征拉曼信号，而~1600 cm -1处(石墨带)的特征拉曼信号消失。在1.5-2.5 eV (500-800 nm)范围内检测到广泛的光致发光发射，这是分离的纳米金刚石的典型特征;与没有表面功能化的样品相比，这些发射带随着1-十一烯的附着而变得更窄。观察到的发射可能与纳米金刚石表面的结构紊乱有关。对每个样品的强度、峰位置和频带宽度的温度依赖性进行了表征。
{"title":"Raman and Photoluminescence Spectroscopic Study of 1-Undecene Functionalized Nanodiamonds","authors":"Y. Astuti, N. Poolton, L. Šiller","doi":"10.1557/OPL.2013.1189","DOIUrl":"https://doi.org/10.1557/OPL.2013.1189","url":null,"abstract":"Nanodiamond holds great interest in a variety of optical applications, the properties being correlated with surface modification, and the presence of both impurities and defects (contained either on their surface or within the crystal structure). Undecyl-nanodiamond produced by attachment of 1-undecene onto the nanodiamond surface could be a good candidate as a luminescent marker in the future; therefore, understanding of its optical properties is essential. In this work, the optical properties of the acid-purified nanodiamond and undecyl-nanodiamond were characterised using surface enhanced Raman spectroscopy (SERS) and photoluminescence spectroscopy. The results demonstrate that the characteristic diamond Raman signal at 1330 cm -1 was still observed after chemical surface modification, while the signal at ~1600 cm -1 (attributed to graphite bands) disappeared after the modification. Broad photoluminescence emission is detected in the range 1.5-2.5 eV (500-800 nm), as typically found for isolated nanodiamond; these emission bands became narrower with attachment of 1-undecene as compared to the sample without surface functionalisation. The observed emission could be related to structural disorder on the nanodiamond surface. The temperature dependence of the intensity, peak position and band widths of each sample has been characterised.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"1597 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2013-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1557/OPL.2013.1189","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67107924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-01DOI: 10.1017/IS012004021JKT189
Paweł Gładki, M. Marshall
Multirings are objects like rings but with multi-valued addition. In the present paper we extend results of E. Becker and others concerning orderings of higher level on fields and rings to orderings of higher level on hyperfields and multirings and, in the process of doing this, we establish higher level analogs of the results previously obtained by the second author. In particular, we introduce a class of multirings called l-real reduced multirings, define a natural reflection A ⇝ Q l-red ( A ) from the category of multirings satisfying to the full subcategory of l-real reduced multirings, and provide an elementary first-order description of these objects. The relationship between l-real reduced hyperfields and the spaces of signatures defined by Mulcahy and Powers is also examined.
{"title":"Orderings and signatures of higher level on multirings and hyperfields","authors":"Paweł Gładki, M. Marshall","doi":"10.1017/IS012004021JKT189","DOIUrl":"https://doi.org/10.1017/IS012004021JKT189","url":null,"abstract":"Multirings are objects like rings but with multi-valued addition. In the present paper we extend results of E. Becker and others concerning orderings of higher level on fields and rings to orderings of higher level on hyperfields and multirings and, in the process of doing this, we establish higher level analogs of the results previously obtained by the second author. In particular, we introduce a class of multirings called l-real reduced multirings, define a natural reflection A ⇝ Q l-red ( A ) from the category of multirings satisfying to the full subcategory of l-real reduced multirings, and provide an elementary first-order description of these objects. The relationship between l-real reduced hyperfields and the spaces of signatures defined by Mulcahy and Powers is also examined.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"1 1","pages":"489-518"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012004021JKT189","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-01DOI: 10.1017/IS012004021JKT190
V. Bavula
{"title":"K 1 ( ) and the group of automorphisms of the algebra of one-sided inverses of a polynomial algebra in two variables","authors":"V. Bavula","doi":"10.1017/IS012004021JKT190","DOIUrl":"https://doi.org/10.1017/IS012004021JKT190","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"10 1","pages":"583-601"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012004021JKT190","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-11-30DOI: 10.1017/IS011011011JKT195
Simon Covez
{"title":"On the conjectural Leibniz cohomology for groups","authors":"Simon Covez","doi":"10.1017/IS011011011JKT195","DOIUrl":"https://doi.org/10.1017/IS011011011JKT195","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"29 1","pages":"519-563"},"PeriodicalIF":0.0,"publicationDate":"2012-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74047302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-11-18DOI: 10.1017/IS014006012JKT270
A. Connes, C. Consani
We show that for a smooth, projective variety X defined over a number field K, cyclic homology with coefficients in the ringA∞ = Q ν|∞ Kν, provides the right theory to obtain, using the λ-operations, Serre’s archimedean local factors of the complex Lfunction of X as regularized determinants. Contents
{"title":"Cyclic homology, Serre's local factors and the -operations","authors":"A. Connes, C. Consani","doi":"10.1017/IS014006012JKT270","DOIUrl":"https://doi.org/10.1017/IS014006012JKT270","url":null,"abstract":"We show that for a smooth, projective variety X defined over a number field K, cyclic homology with coefficients in the ringA∞ = Q ν|∞ Kν, provides the right theory to obtain, using the λ-operations, Serre’s archimedean local factors of the complex Lfunction of X as regularized determinants. Contents","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"14 1","pages":"1-45"},"PeriodicalIF":0.0,"publicationDate":"2012-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS014006012JKT270","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-31DOI: 10.1017/IS014003007JKT257
Toshiro Hiranouchi
We introduce a Milnor type $K$-group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's $K$-group. We show that the $K$-group associated to the additive group and $q$ multiplicative groups of a field is isomorphic to the space of absolute Kahler differentials of degree $q$ of the field, thus giving us a geometric interpretation of the space of absolute Kahler differentials. We also show that the $K$-group associated to the additive group and Jacobian variety of a curve is isomorphic to the homology group of a certain complex.
{"title":"An additive variant of Somekawa's K-groups and Kähler differentials","authors":"Toshiro Hiranouchi","doi":"10.1017/IS014003007JKT257","DOIUrl":"https://doi.org/10.1017/IS014003007JKT257","url":null,"abstract":"We introduce a Milnor type $K$-group associated to commutative algebraic groups over a perfect field. It is an additive variant of Somekawa's $K$-group. We show that the $K$-group associated to the additive group and $q$ multiplicative groups of a field is isomorphic to the space of absolute Kahler differentials of degree $q$ of the field, thus giving us a geometric interpretation of the space of absolute Kahler differentials. We also show that the $K$-group associated to the additive group and Jacobian variety of a curve is isomorphic to the homology group of a certain complex.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"2019 1","pages":"481-516"},"PeriodicalIF":0.0,"publicationDate":"2012-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS014003007JKT257","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-08-30DOI: 10.1017/IS014006030JKT273
Hailong Dao, Kazuhiko Kurano
Let ( A , ) be a local hypersurface with an isolated singularity. We show that Hochster's theta pairing θ A vanishes on elements that are numerically equivalent to zero in the Grothendieck group of A under the mild assumption that Spec A admits a resolution of singularities. This extends a result by Celikbas-Walker. We also prove that when dim A = 3, Hochster's theta pairing is positive semi-definite. These results combine to show that the counter-example of Dutta-Hochster-McLaughlin to the general vanishing of Serre's intersection multiplicity exists for any three dimensional isolated hypersurface singularity that is not a UFD and has a desingularization. We also show that, if A is three dimensional isolated hypersurface singularity that has a desingularization, the divisor class group is finitely generated torsion-free. Our method involves showing that θ A gives a bivariant class for the morphism Spec ( A / ) → Spec A .
设(A，)为具有孤立奇点的局部超曲面。我们证明了Hochster的θ对θ A在A的Grothendieck群中在数值上等于零的元素上消失，假设Spec A允许奇点的分辨。这扩展了Celikbas-Walker的一个结果。我们还证明了当dim A = 3时，Hochster配对是正半定的。这些结果结合起来表明，对于任何非UFD且具有非具体化的三维孤立超曲面奇点，存在Dutta-Hochster-McLaughlin关于Serre相交多重性一般消失的反例。我们还证明，如果A是具有去奇异性的三维孤立超曲面奇点，则除数类群是有限生成的无扭转。我们的方法是证明θ A给出了态射Spec (A /)→Spec A的一个双变类。
{"title":"Hochster's theta pairing and numerical equivalence","authors":"Hailong Dao, Kazuhiko Kurano","doi":"10.1017/IS014006030JKT273","DOIUrl":"https://doi.org/10.1017/IS014006030JKT273","url":null,"abstract":"Let ( A , ) be a local hypersurface with an isolated singularity. We show that Hochster's theta pairing θ A vanishes on elements that are numerically equivalent to zero in the Grothendieck group of A under the mild assumption that Spec A admits a resolution of singularities. This extends a result by Celikbas-Walker. We also prove that when dim A = 3, Hochster's theta pairing is positive semi-definite. These results combine to show that the counter-example of Dutta-Hochster-McLaughlin to the general vanishing of Serre's intersection multiplicity exists for any three dimensional isolated hypersurface singularity that is not a UFD and has a desingularization. We also show that, if A is three dimensional isolated hypersurface singularity that has a desingularization, the divisor class group is finitely generated torsion-free. Our method involves showing that θ A gives a bivariant class for the morphism Spec ( A / ) → Spec A .","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"14 1","pages":"495-525"},"PeriodicalIF":0.0,"publicationDate":"2012-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS014006030JKT273","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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