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arXiv: K-Theory and Homology最新文献

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Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods 代数K -理论，汇编映射，控制代数，和跟踪方法
arXiv: K-Theory and Homology Pub Date : 2017-02-07 DOI: 10.1515/9783110452150-001
H. Reich, Marco Varisco
{"title":"Algebraic $K$-theory, assembly maps, controlled algebra, and trace methods","authors":"H. Reich, Marco Varisco","doi":"10.1515/9783110452150-001","DOIUrl":"https://doi.org/10.1515/9783110452150-001","url":null,"abstract":"We give a concise introduction to the Farrell-Jones Conjecture in algebraic $K$-theory and to some of its applications. We survey the current status of the conjecture, and we illustrate the two main tools that are used to attack it: controlled algebra and trace methods.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132638809","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}
引用次数: 11
Adams Operations on Matrix Factorizations 矩阵分解的Adams运算
arXiv: K-Theory and Homology Pub Date : 2016-10-31 DOI: 10.2140/ant.2017.11.2165
Michael K. Brown, C. Miller, Peder Thompson, M. Walker
{"title":"Adams Operations on Matrix Factorizations","authors":"Michael K. Brown, C. Miller, Peder Thompson, M. Walker","doi":"10.2140/ant.2017.11.2165","DOIUrl":"https://doi.org/10.2140/ant.2017.11.2165","url":null,"abstract":"We define Adams operations on matrix factorizations, and we show these operations enjoy analogues of several key properties of the Adams operations on perfect complexes with support developed by Gillet-Soul'e in their paper \"Intersection Theory Using Adams Operations\". As an application, we give a proof of a conjecture of Dao-Kurano concerning the vanishing of Hochster's theta invariant.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113962949","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}
引用次数: 5
Fixed points of the equivariant algebraic $K$-theory of spaces 等变代数K -空间理论的不动点
arXiv: K-Theory and Homology Pub Date : 2016-09-15 DOI: 10.1090/PROC/13584
Bernard Badzioch, Wojciech Dorabiała
{"title":"Fixed points of the equivariant algebraic $K$-theory of spaces","authors":"Bernard Badzioch, Wojciech Dorabiała","doi":"10.1090/PROC/13584","DOIUrl":"https://doi.org/10.1090/PROC/13584","url":null,"abstract":"In a recent work Malkiewich and Merling proposed a definition of the equivariant $K$-theory of spaces for spaces equipped with an action of a finite group. We show that the fixed points of this spectrum admit a tom Dieck-type splitting. We also show that this splitting is compatible with the splitting of the equivariant suspension spectrum. The first of these results has been obtained independently by John Rognes.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134460899","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}
引用次数: 2
Complex of injective words revisited 重访了反语复合体
arXiv: K-Theory and Homology Pub Date : 2016-08-16 DOI: 10.36045/BBMS/1489888818
Wee Liang Gan
{"title":"Complex of injective words revisited","authors":"Wee Liang Gan","doi":"10.36045/BBMS/1489888818","DOIUrl":"https://doi.org/10.36045/BBMS/1489888818","url":null,"abstract":"We give a simple proof that (a generalization of) the complex of injective words has vanishing homology in all except the top degree.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128286785","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}
引用次数: 5
Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II 与Kac-Moody类群相关的标志品种的$T$-等变$K$-理论的正性ⅱ
arXiv: K-Theory and Homology Pub Date : 2016-07-12 DOI: 10.1090/ERT/494
Seth Baldwin, Shrawan Kumar
{"title":"Positivity in $T$-equivariant $K$-theory of flag varieties associated to Kac-Moody groups II","authors":"Seth Baldwin, Shrawan Kumar","doi":"10.1090/ERT/494","DOIUrl":"https://doi.org/10.1090/ERT/494","url":null,"abstract":"We prove sign-alternation of the structure constants in the basis of structure sheaves of opposite Schubert varieties in the torus-equivariant Grothendieck group of coherent sheaves on the flag varieties $G/P$ associated to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic subgroup. This generalizes the work of Anderson-Griffeth-Miller from the finite case to the general Kac-Moody case, and affirmatively answers a conjecture of Lam-Schilling-Shimozono regarding the signs of the structure constants in the case of the affine Grassmannian.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127417559","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}
引用次数: 13
Cyclic vs mixed homology 循环与混合同源
arXiv: K-Theory and Homology Pub Date : 2016-07-07 DOI: 10.4310/HHA.2018.V20.N1.A14
U. Kraehmer, Dylan Madden
{"title":"Cyclic vs mixed homology","authors":"U. Kraehmer, Dylan Madden","doi":"10.4310/HHA.2018.V20.N1.A14","DOIUrl":"https://doi.org/10.4310/HHA.2018.V20.N1.A14","url":null,"abstract":"The spectral theory of the Karoubi operator due to Cuntz and Quillen is extended to general mixed (duchain) complexes, that is, chain complexes which are simultaneously cochain complexes. Connes' coboundary map B can be viewed as a perturbation of the noncommutative De Rham differential d by a polynomial in the Karoubi operator. The homological impact of such perturbations is expressed in terms of two short exact sequences.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126143927","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}
引用次数: 2
Exterior power operations on higher $K$-groups via binary complexes 通过二元复合体对高K -群的外部幂运算
arXiv: K-Theory and Homology Pub Date : 2016-07-06 DOI: 10.2140/akt.2017.2.409
Tom Harris, Bernhard Kock, L. Taelman
{"title":"Exterior power operations on higher $K$-groups via binary complexes","authors":"Tom Harris, Bernhard Kock, L. Taelman","doi":"10.2140/akt.2017.2.409","DOIUrl":"https://doi.org/10.2140/akt.2017.2.409","url":null,"abstract":"We use Grayson's binary multicomplex presentation of algebraic $K$-theory to give a new construction of exterior power operations on the higher $K$-groups of a (quasi-compact) scheme. We show that these operations satisfy the axioms of a $lambda$-ring, including the product and composition laws. To prove the composition law we show that the Grothendieck group of the exact category of integral polynomial functors is the universal $lambda$-ring on one generator.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133739358","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}
引用次数: 9
Cohomology and deformations of Courant pairs Courant对的上同调与变形
arXiv: K-Theory and Homology Pub Date : 2016-06-06 DOI: 10.4172/1736-4337.1000281
A. Mandal, S. K. Mishra
{"title":"Cohomology and deformations of Courant pairs","authors":"A. Mandal, S. K. Mishra","doi":"10.4172/1736-4337.1000281","DOIUrl":"https://doi.org/10.4172/1736-4337.1000281","url":null,"abstract":"In this note we define a notion of Courant pair as a Courant algebra over the Lie algebra of linear derivations on an associative algebra. We study formal deformations of Courant pairs by constructing a cohomology bicomplex with coefficients in a module from the cochain complexes defining Hochschild cohomology and Leibniz cohomology.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115947997","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}
引用次数: 1
On constructing weight structures and extending them to idempotent extensions 论权结构的构造及其幂等扩展
arXiv: K-Theory and Homology Pub Date : 2016-05-26 DOI: 10.4310/HHA.2018.V20.N1.A3
M. Bondarko, V. Sosnilo
{"title":"On constructing weight structures and extending them to idempotent extensions","authors":"M. Bondarko, V. Sosnilo","doi":"10.4310/HHA.2018.V20.N1.A3","DOIUrl":"https://doi.org/10.4310/HHA.2018.V20.N1.A3","url":null,"abstract":"We describe a new method for constructing a weight structure $w$ on a triangulated category $C$. \u0000For a given $C$ and $w$ it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of retracts of objects of $C$ (i.e., of subcategories of the Karoubi envelope of $C$ that contain $C$; we call them idempotent extensions of $C$) such that $w$ extends to them. In particular, any bounded above or below $w$ extends to any idempotent extension of $C$. We also discuss the applications of our results to certain triangulated categories of (\"relative\") motives.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122658558","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}
引用次数: 30
Hochschild Cohomology of Reduced Incidence Algebras 约关联代数的Hochschild上同调
arXiv: K-Theory and Homology Pub Date : 2016-05-22 DOI: 10.1142/S0219498817501687
M. Kanuni, A. Kaygun, S. Sutlu
{"title":"Hochschild Cohomology of Reduced Incidence Algebras","authors":"M. Kanuni, A. Kaygun, S. Sutlu","doi":"10.1142/S0219498817501687","DOIUrl":"https://doi.org/10.1142/S0219498817501687","url":null,"abstract":"We compute the Hochschild cohomology of the reduced incidence algebras such as the algebra of formal power series, the algebra of exponential power series, the algebra of Eulerian power series, and the algebra of formal Dirichlet series. We achieve the result by carrying out the computation on the coalgebra ${rm Cotor}$-groups of their pre-dual coalgebras. Using the same coalgebraic machinery, we further identify the Hochschild cohomology groups of an incidence algebra associated to a quiver with the ${rm Ext}$-groups of the incidence algebra associated to a suspension of the quiver.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129400918","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}
引用次数: 0
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