Pub Date : 2012-08-24DOI: 10.1017/IS014007001JKT274
Antti J. Harju, J. Mickelsson
Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on T and an integral class in H(M,Z). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups. Msc: 19L50, 53C08, 81T70
{"title":"Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class","authors":"Antti J. Harju, J. Mickelsson","doi":"10.1017/IS014007001JKT274","DOIUrl":"https://doi.org/10.1017/IS014007001JKT274","url":null,"abstract":"Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on T and an integral class in H(M,Z). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups. Msc: 19L50, 53C08, 81T70","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"47 27 1","pages":"247-272"},"PeriodicalIF":0.0,"publicationDate":"2012-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS014007001JKT274","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668932","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 : 2012-08-01DOI: 10.1017/IS011010023JKT164
B. Williams
The main result of this paper is a computation of the motivic cohomology of varieties of n m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general linear group-scheme with a Tate suspension of a space which isA 1 -equivalent to projective n 1-space with a disjoint basepoint.
{"title":"The Motivic Cohomology of Stiefel Varieties","authors":"B. Williams","doi":"10.1017/IS011010023JKT164","DOIUrl":"https://doi.org/10.1017/IS011010023JKT164","url":null,"abstract":"The main result of this paper is a computation of the motivic cohomology of varieties of n m-matrices of of rank m, including both the ring structure and the action of the reduced power operations. The argument proceeds by a comparison of the general linear group-scheme with a Tate suspension of a space which isA 1 -equivalent to projective n 1-space with a disjoint basepoint.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"76 1","pages":"141-163"},"PeriodicalIF":0.0,"publicationDate":"2012-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011010023JKT164","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666476","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 : 2012-08-01DOI: 10.1017/IS012001013JKT182
V. Petrov, N. Semenov
This article gives a complete classification of generically split projective homogeneous varieties. This project was begun in our previous article [PS10], but here we remove all restrictions on the characteristic of the base field, give a new uniform proof that works in all cases and in particular includes the case PGO2n which was missing in [PS10]. MSC2010: 20G15, 14C15
{"title":"Generically split projective homogeneous varieties. II","authors":"V. Petrov, N. Semenov","doi":"10.1017/IS012001013JKT182","DOIUrl":"https://doi.org/10.1017/IS012001013JKT182","url":null,"abstract":"This article gives a complete classification of generically split projective homogeneous varieties. This project was begun in our previous article [PS10], but here we remove all restrictions on the characteristic of the base field, give a new uniform proof that works in all cases and in particular includes the case PGO2n which was missing in [PS10]. MSC2010: 20G15, 14C15","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"10 1","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2012-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012001013JKT182","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666778","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 : 2012-06-01DOI: 10.1017/IS011010022JKT170
R. Deeley
{"title":"Geometric K -homology with coefficients I: ℤ/ k ℤ-cycles and Bockstein sequence","authors":"R. Deeley","doi":"10.1017/IS011010022JKT170","DOIUrl":"https://doi.org/10.1017/IS011010022JKT170","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"537-564"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011010022JKT170","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666439","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 : 2012-06-01DOI: 10.1017/IS011010026JKT165
Georg Tamme
In this paper we prove the p-adic analogue of a result of Hamida [11], namely that the p-adic Borel regulator introduced by Huber and Kings for the Ktheory of a p-adic number field equals Karoubi’s p-adic regulator up to an explicit rational factor.
{"title":"Comparison of Karoubi's regulator and the p-adic Borel regulator","authors":"Georg Tamme","doi":"10.1017/IS011010026JKT165","DOIUrl":"https://doi.org/10.1017/IS011010026JKT165","url":null,"abstract":"In this paper we prove the p-adic analogue of a result of Hamida [11], namely \u0000that the p-adic Borel regulator introduced by Huber and Kings for the Ktheory \u0000of a p-adic number field equals Karoubi’s p-adic regulator up to an \u0000explicit rational factor.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"54 1","pages":"579-600"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011010026JKT165","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666565","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 : 2012-06-01DOI: 10.1017/IS011011006JKT174
Kenichiro Kimura, Shungen Kimura, N. Takahashi
Let C be a pseudo-abelian symmetric monoidal category, and X a Schur-finite object of C . We study the problem of rationality of the motivic zeta function ζ x(t) of X . Since the coefficient ring is not a field, there are several variants of rationality — uniform, global, determinantal and pointwise rationality. We show that ζ x(t) is determinantally rational, and we give an example of C and X for which the motivic zeta function is not uniformly rational.
{"title":"Motivic zeta functions in additive monoidal categories","authors":"Kenichiro Kimura, Shungen Kimura, N. Takahashi","doi":"10.1017/IS011011006JKT174","DOIUrl":"https://doi.org/10.1017/IS011011006JKT174","url":null,"abstract":"Let C be a pseudo-abelian symmetric monoidal category, and X a Schur-finite object of C . We study the problem of rationality of the motivic zeta function ζ x(t) of X . Since the coefficient ring is not a field, there are several variants of rationality — uniform, global, determinantal and pointwise rationality. We show that ζ x(t) is determinantally rational, and we give an example of C and X for which the motivic zeta function is not uniformly rational.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"459-473"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011011006JKT174","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666693","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 : 2012-06-01DOI: 10.1017/IS011011001JKT171
M. Benameur, J. Heitsch
We prove that a leafwise homotopy equivalence between compact foliated manifolds induces a well defined bounded operator between all Sobolov spaces of leafwise (for the natural foliations of the graphs of the original foliations) differential forms with coefficients in a leafwise flat bundle. We further prove that the associated map on the leafwise reduced L 2 cohomology is an isomorphism which only depends on the leafwise homotopy class of the homotopy equivalence.
{"title":"Leafwise homotopy equivalences and leafwise Sobolov spaces","authors":"M. Benameur, J. Heitsch","doi":"10.1017/IS011011001JKT171","DOIUrl":"https://doi.org/10.1017/IS011011001JKT171","url":null,"abstract":"We prove that a leafwise homotopy equivalence between compact foliated manifolds induces a well defined bounded operator between all Sobolov spaces of leafwise (for the natural foliations of the graphs of the original foliations) differential forms with coefficients in a leafwise flat bundle. We further prove that the associated map on the leafwise reduced L 2 cohomology is an isomorphism which only depends on the leafwise homotopy class of the homotopy equivalence.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"51 1","pages":"503-520"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011011001JKT171","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666935","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 : 2012-06-01DOI: 10.1017/IS011011005JKT166
M. Morrow
The norm map on the Milnor K-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.
{"title":"Continuity of the norm map on Milnor K-theory","authors":"M. Morrow","doi":"10.1017/IS011011005JKT166","DOIUrl":"https://doi.org/10.1017/IS011011005JKT166","url":null,"abstract":"The norm map on the Milnor K-groups of a finite extension of complete, discrete valuation fields is continuous with respect to the unit group filtrations. The only proof in the literature, due to K. Kato, uses semi-global methods. Here we present an elementary algebraic proof.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"10 1","pages":"565-577"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011011005JKT166","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56667047","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 : 2012-06-01DOI: 10.1017/IS011005004JKT158
O. King, G. Robertson
Let Γ be an A 2 subgroup of PGL 3 ( ), where is a local field with residue field of order q . The module of coinvariants C ( ,ℤ) Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1] K 0 in the K-theory of the (full) crossed product C *-algebra C (Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL 3 ( ). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.
{"title":"On the K-theory of boundary C *-algebras of à 2 groups","authors":"O. King, G. Robertson","doi":"10.1017/IS011005004JKT158","DOIUrl":"https://doi.org/10.1017/IS011005004JKT158","url":null,"abstract":"Let Γ be an A 2 subgroup of PGL 3 ( ), where is a local field with residue field of order q . The module of coinvariants C ( ,ℤ) Γ is shown to be finite, where is the projective plane over . If the group Γ is of Tits type and if q ≢ 1 (mod 3) then the exact value of the order of the class [1] K 0 in the K-theory of the (full) crossed product C *-algebra C (Ω) ⋊ Γ is determined, where Ω is the Furstenberg boundary of PGL 3 ( ). For groups of Tits type, this verifies a conjecture of G. Robertson and T. Steger.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"521-536"},"PeriodicalIF":0.0,"publicationDate":"2012-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011005004JKT158","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666557","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 : 2012-04-01DOI: 10.1017/IS011003006JKT135
J. Assim, A. Movahhedi
{"title":"Norm index formula for the Tate Kernels and applications","authors":"J. Assim, A. Movahhedi","doi":"10.1017/IS011003006JKT135","DOIUrl":"https://doi.org/10.1017/IS011003006JKT135","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"359-383"},"PeriodicalIF":0.0,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011003006JKT135","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666079","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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