发布求助
文献互助 智能选刊 最新文献

arXiv - MATH - K-Theory and Homology最新文献

筛选
英文 中文
Segal K-theory of vector spaces with an automorphism 有自动形态的向量空间的 Segal K 理论
arXiv - MATH - K-Theory and Homology Pub Date : 2024-07-01 DOI: arxiv-2407.01482
Andrea Bianchi, Florian Kranhold
{"title":"Segal K-theory of vector spaces with an automorphism","authors":"Andrea Bianchi, Florian Kranhold","doi":"arxiv-2407.01482","DOIUrl":"https://doi.org/arxiv-2407.01482","url":null,"abstract":"We describe the Segal $K$-theory of the symmetric monoidal category of\u0000finite-dimensional vector spaces over a perfect field $mathbb{F}$ together\u0000with an automorphism, or, equivalently, the group-completion of the\u0000$E_infty$-algebra of maps from $S^1$ to the disjoint union of classifying\u0000spaces $mathrm{BGL}_d(mathbb F)$, in terms of the $K$-theory of finite field\u0000extensions of $mathbb{F}$. A key ingredient for this is a computation of the\u0000Segal $K$-theory of the category of finite-dimensional vector spaces with a\u0000nilpotent endomorphism, which we do over any field $mathbb F$. We also discuss\u0000the topological cases of $mathbb F =mathbb C,mathbb R$.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511482","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
Notes on Siegfried Bosch's Algebraic Geometry and Commutative Algebra (dedicated to Grothendieck) 西格弗里德-博什的《代数几何与交换代数》笔记（献给格罗登第克）
arXiv - MATH - K-Theory and Homology Pub Date : 2024-07-01 DOI: arxiv-2407.01829
Eric Schmid
{"title":"Notes on Siegfried Bosch's Algebraic Geometry and Commutative Algebra (dedicated to Grothendieck)","authors":"Eric Schmid","doi":"arxiv-2407.01829","DOIUrl":"https://doi.org/arxiv-2407.01829","url":null,"abstract":"Notes on Commutative Alegbra and Algebraic Geometry covering rings, ideals,\u0000modules, presheaves, sheaves, schemes, homological algebra, 'etale cohomology\u0000and further topics that are more advanced.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"61 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511491","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
A criterion for slope 1 homological stability 斜率 1 同调稳定性标准
arXiv - MATH - K-Theory and Homology Pub Date : 2024-07-01 DOI: arxiv-2407.01124
Mikala Ørsnes Jansen, Jeremy Miller
{"title":"A criterion for slope 1 homological stability","authors":"Mikala Ørsnes Jansen, Jeremy Miller","doi":"arxiv-2407.01124","DOIUrl":"https://doi.org/arxiv-2407.01124","url":null,"abstract":"We show that for nice enough $mathbb{N}$-graded $mathbb{E}_2$-algebras, a\u0000diagonal vanishing line in $mathbb{E}_1$-homology of gives rise to slope $1$\u0000homological stability. This is an integral version of a result by\u0000Kupers-Miller-Patzt.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511481","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
The Galois-equivariant $K$-theory of finite fields 有限域的伽罗瓦-参数 $K$ 理论
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-27 DOI: arxiv-2406.19481
David Chan, Chase Vogeli
{"title":"The Galois-equivariant $K$-theory of finite fields","authors":"David Chan, Chase Vogeli","doi":"arxiv-2406.19481","DOIUrl":"https://doi.org/arxiv-2406.19481","url":null,"abstract":"We compute the $RO(G)$-graded equivariant algebraic $K$-groups of a finite\u0000field with an action by its Galois group $G$. Specifically, we show these\u0000$K$-groups split as the sum of an explicitly computable term and the\u0000well-studied $RO(G)$-graded coefficient groups of the equivariant\u0000Eilenberg--MacLane spectrum $Hunderline{mathbb Z}$. Our comparison between\u0000the equivariant $K$-theory spectrum and $Hunderline{mathbb Z}$ further shows\u0000they share the same Tate spectra and geometric fixed point spectra. In the case\u0000where $G$ has prime order, we provide an explicit presentation of the\u0000equivariant $K$-groups.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"181 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511483","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
Simple homotopy invariance of the loop coproduct 环共积的简单同调不变性
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-27 DOI: arxiv-2406.19326
Florian Naef, Pavel Safronov
{"title":"Simple homotopy invariance of the loop coproduct","authors":"Florian Naef, Pavel Safronov","doi":"arxiv-2406.19326","DOIUrl":"https://doi.org/arxiv-2406.19326","url":null,"abstract":"We prove a transformation formula for the Goresky-Hingston loop coproduct in\u0000string topology under homotopy equivalences of manifolds. The formula involves\u0000the trace of the Whitehead torsion of the homotopy equivalence. In particular,\u0000it implies that the loop coproduct is invariant under simple homotopy\u0000equivalences. In a sense, our results determine the Dennis trace of the simple\u0000homotopy type of a closed manifold from its framed configuration spaces of\u0000$leq 2$ points. We also explain how the loop coproduct arises as a secondary\u0000operation in a 2-dimensional TQFT which elucidates a topological origin of the\u0000transformation formula.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"152 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511484","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
A model structure and Hopf-cyclic theory on the category of coequivariant modules over a comodule algebra 组合代数上的共变模块范畴的模型结构与霍普循环理论
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-24 DOI: arxiv-2406.16329
Mariko Ohara
{"title":"A model structure and Hopf-cyclic theory on the category of coequivariant modules over a comodule algebra","authors":"Mariko Ohara","doi":"arxiv-2406.16329","DOIUrl":"https://doi.org/arxiv-2406.16329","url":null,"abstract":"Let H be a coFrobenius Hopf algebra over a field k. Let A be a right\u0000H-comodule algebra over k. We recall that the category of right H-comodules admits a certain model\u0000structure whose homotopy category is equivalent to the stable category of right\u0000H-comodules given in Farina's paper. In the first part of this paper, we show\u0000that the category of left A-module objects in the category of right H-comodules\u0000admits a model structure, which becomes a model subcategory of the category of\u0000H*-equivariant A-modules endowed with a model structure given in the author's\u0000previous paper if H is finite dimensional with a certain assumption. Note that\u0000this category is not a Frobenius category in general. We also construct a\u0000functorial cofibrant replacement by proceeding the similar argument as in Qi's\u0000paper. In the latter half of this paper, we see that cyclic H-comodules which\u0000give Hopf-cyclic (co)homology with coefficients in Hopf H-modules are\u0000contructible in the homotopy category of right H-comodules, and we investigate\u0000a Hopf-cyclic (co)homology in slightly modified setting by assuming A a right\u0000H-comodule k-Hopf algebra with H-colinear bijective antipode in stable category\u0000of right H-comodules and give an analogue of the characteristic map. We remark\u0000that, as an expansion of an idea of taking trivial comodule k as the\u0000coefficients, if we take an A-coinvariant part of M assuming M a Hopf A-module\u0000in the category of right H-comodules, we have the degree shift of cyclic\u0000modules.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511485","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
Computations regarding the torsion homology of Oeljeklaus-Toma manifolds 有关奥勒耶克劳斯-托马流形扭转同调的计算
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-21 DOI: arxiv-2406.14942
Dung Phuong PhanGAATI, UPF, Tuan Anh BuiHCMUS, Alexander D. RahmGAATI, UPF
{"title":"Computations regarding the torsion homology of Oeljeklaus-Toma manifolds","authors":"Dung Phuong PhanGAATI, UPF, Tuan Anh BuiHCMUS, Alexander D. RahmGAATI, UPF","doi":"arxiv-2406.14942","DOIUrl":"https://doi.org/arxiv-2406.14942","url":null,"abstract":"This article investigates the torsion homology behaviour in towers of\u0000Oeljeklaus-Toma (OT) manifolds. This adapts an idea of Silver and Williams from\u0000knot theory to OT-manifolds and extends it to higher degree homology groups.In\u0000the case of surfaces, i.e. Inoue surfaces of type $S^{0}$, the torsion grows\u0000exponentially in both $H_1$ and $H_2$ according to a parameters which already\u0000plays a role in Inoue's classical paper. This motivates running example\u0000calculations in all homological degrees.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"206 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511486","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
A Geometric Splitting of the Motive of $textrm{GL}_n$ $textrm{GL}_n$ 动机的几何拆分
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-20 DOI: arxiv-2406.14687
W. Sebastian Gant
{"title":"A Geometric Splitting of the Motive of $textrm{GL}_n$","authors":"W. Sebastian Gant","doi":"arxiv-2406.14687","DOIUrl":"https://doi.org/arxiv-2406.14687","url":null,"abstract":"A paper by Haynes Miller shows that there is a filtration on the unitary\u0000groups that splits in the stable homotopy category, where the stable summands\u0000are certain Thom spaces over Grassmannians. We give an algebraic version of\u0000this result in the context of Voevodsky's tensor triangulated category of\u0000stable motivic complexes $textbf{DM}(k,R)$, where $k$ is a field.\u0000Specifically, we show that there are algebraic analogs of the Thom spaces\u0000appearing in Miller's splitting that give rise to an analogous splitting of the\u0000motive $M(textrm{GL}_n)$ in $textbf{DM}(k,R)$, where $textrm{GL}_n$ is the\u0000general linear group scheme over $k$.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511487","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
Finite group actions on dg categories and Hochschild homology dg 类上的有限群作用与霍赫希尔德同源性
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-19 DOI: arxiv-2406.13866
Ville Nordstrom
{"title":"Finite group actions on dg categories and Hochschild homology","authors":"Ville Nordstrom","doi":"arxiv-2406.13866","DOIUrl":"https://doi.org/arxiv-2406.13866","url":null,"abstract":"We prove a decomposition of the Hochschild homology groups of the equivariant\u0000dg category $mathscr{C}^G$ associated to a small dg category $mathscr{C}$\u0000with direct sums on which a finite group $G$ acts. When the ground field is\u0000$mathbb{C}$ this decomposition is related to a categorical action of\u0000$text{Rep}(G)$ on $mathscr{C}^G$ and the resulting action of the\u0000representation ring $R_mathbb{C}(G)$ on $HH_bullet(mathscr{C}^G)$.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511488","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
Stratification of Derived Categories of Tate Motives 泰特动机衍生类别的分层
arXiv - MATH - K-Theory and Homology Pub Date : 2024-06-18 DOI: arxiv-2406.13088
David Rubinstein
{"title":"Stratification of Derived Categories of Tate Motives","authors":"David Rubinstein","doi":"arxiv-2406.13088","DOIUrl":"https://doi.org/arxiv-2406.13088","url":null,"abstract":"We classify the localizing tensor ideals of the derived categories of mixed\u0000Tate motives over certain algebraically closed fields. More precisely, we prove\u0000that these categories are stratified in the sense of Barthel, Heard and\u0000Sanders. A key ingredient in the proof is the development of a new technique\u0000for transporting stratification between categories by means of Brown--Adams\u0000representability, which may be of independent interest.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141511498","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信