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
Unstable algebraic K-theory: homological stability and other observations 不稳定的代数 K 理论：同调稳定性及其他观察结果
arXiv - MATH - K-Theory and Homology Pub Date : 2024-05-03 DOI: arxiv-2405.02065
Mikala Ørsnes Jansen
{"title":"Unstable algebraic K-theory: homological stability and other observations","authors":"Mikala Ørsnes Jansen","doi":"arxiv-2405.02065","DOIUrl":"https://doi.org/arxiv-2405.02065","url":null,"abstract":"We investigate stability properties of the reductive Borel-Serre categories;\u0000these were introduced as a model for unstable algebraic K-theory in previous\u0000work. We see that they exhibit better homological stability properties than the\u0000general linear groups. We also show that they provide an explicit model for\u0000Yuan's partial algebraic K-theory.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882591","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
Real spin bordism and orientations of topological $mathrm{K}$-theory 拓扑$mathrm{K}$理论的实自旋边界和定向
arXiv - MATH - K-Theory and Homology Pub Date : 2024-05-02 DOI: arxiv-2405.00963
Zachary Halladay, Yigal Kamel
{"title":"Real spin bordism and orientations of topological $mathrm{K}$-theory","authors":"Zachary Halladay, Yigal Kamel","doi":"arxiv-2405.00963","DOIUrl":"https://doi.org/arxiv-2405.00963","url":null,"abstract":"We construct a commutative orthogonal $C_2$-ring spectrum,\u0000$mathrm{MSpin}^c_{mathbb{R}}$, along with a $C_2$-$E_{infty}$-orientation\u0000$mathrm{MSpin}^c_{mathbb{R}} to mathrm{KU}_{mathbb{R}}$ of Atiyah's Real\u0000K-theory. Further, we define $E_{infty}$-maps $mathrm{MSpin} to\u0000(mathrm{MSpin}^c_{mathbb{R}})^{C_2}$ and $mathrm{MU}_{mathbb{R}} to\u0000mathrm{MSpin}^c_{mathbb{R}}$, which are used to recover the three well-known\u0000orientations of topological $mathrm{K}$-theory, $mathrm{MSpin}^c to\u0000mathrm{KU}$, $mathrm{MSpin} to mathrm{KO}$, and $mathrm{MU}_{mathbb{R}}\u0000to mathrm{KU}_{mathbb{R}}$, from the map $mathrm{MSpin}^c_{mathbb{R}} to\u0000mathrm{KU}_{mathbb{R}}$. We also show that the integrality of the\u0000$hat{A}$-genus on spin manifolds provides an obstruction for the fixed points\u0000$(mathrm{MSpin}^c_{mathbb{R}})^{C_2}$ to be equivalent to $mathrm{MSpin}$,\u0000using the Mackey functor structure of\u0000$underline{pi}_*mathrm{MSpin}^c_{mathbb{R}}$. In particular, the usual map\u0000$mathrm{MSpin} to mathrm{MSpin}^c$ does not arise as the inclusion of fixed\u0000points for any $C_2$-$E_{infty}$-ring spectrum.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"125 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833945","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
An obstruction theory for strictly commutative algebras in positive characteristic 正特征严格交换代数的阻塞理论
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-25 DOI: arxiv-2404.16681
Oisín Flynn-Connolly
{"title":"An obstruction theory for strictly commutative algebras in positive characteristic","authors":"Oisín Flynn-Connolly","doi":"arxiv-2404.16681","DOIUrl":"https://doi.org/arxiv-2404.16681","url":null,"abstract":"This is the first in a sequence of articles exploring the relationship\u0000between commutative algebras and $E_infty$-algebras in characteristic $p$ and\u0000mixed characteristic. In this paper we lay the groundwork by defining a new\u0000class of cohomology operations over $mathbb F_p$ called cotriple products,\u0000generalising Massey products. We compute the secondary cohomology operations\u0000for a strictly commutative dg-algebra and the obstruction theories these\u0000induce, constructing several counterexamples to characteristic 0 behaviour, one\u0000of which answers a question of Campos, Petersen, Robert-Nicoud and Wierstra. We\u0000construct some families of higher cotriple products and comment on their\u0000behaviour. Finally, we distingush a subclass of cotriple products that we call\u0000higher Steenrod operation and conclude with our main theorem, which says that\u0000$E_infty$-algebras can be rectified if and only if the higher Steenrod\u0000operations vanish coherently.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"138 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798728","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 complex K ring of the flip Stiefel manifolds 翻转斯蒂费尔流形的复 K 环
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-24 DOI: arxiv-2404.15803
Samik Basu, Shilpa Gondhali, Fathima Safikaa
{"title":"The complex K ring of the flip Stiefel manifolds","authors":"Samik Basu, Shilpa Gondhali, Fathima Safikaa","doi":"arxiv-2404.15803","DOIUrl":"https://doi.org/arxiv-2404.15803","url":null,"abstract":"The flip Stiefel manifolds (FV_{m,2s}) are defined as the quotient of the\u0000real Stiefel manifolds (V_{m,2s}) induced by the simultaneous pairwise flipping\u0000of the co-ordinates by the cyclic group of order 2. We calculate the complex\u0000(K)-ring of the flip Stiefel manifolds, $K^ast(FV_{m,2s})$, for $s$ even.\u0000Standard techniques involve the representation theory of $Spin(m),$ and the\u0000Hodgkin spectral sequence. However, the non-trivial element inducing the action\u0000doesn't readily yield the desired homomorphisms. Hence, by performing\u0000additional analysis, we settle the question for the case of (s equiv 0 pmod\u00002.)","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798707","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
On the homology of partial group actions 论部分群作用的同源性
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-23 DOI: arxiv-2404.14650
Emmanuel Jerez
{"title":"On the homology of partial group actions","authors":"Emmanuel Jerez","doi":"arxiv-2404.14650","DOIUrl":"https://doi.org/arxiv-2404.14650","url":null,"abstract":"We study the partial group (co)homology of partial group actions using\u0000simplicial methods. We introduce the concept of universal globalization of a\u0000partial group action on a $K$-module and prove that, given a partial\u0000representation of $G$ on $M$, the partial group homology $H^{par}_{bullet}(G,\u0000M)$ is naturally isomorphic to the usual group homology $H_{bullet}(G, KG\u0000otimes_{G_{par}} M)$, where $KG otimes_{G_{par}} M$ is the universal\u0000globalization of the partial group action associated to $M$. We dualize this\u0000result into a cohomological spectral sequence converging to\u0000$H^{bullet}_{par}(G,M)$.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798773","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
Equivariant $K$-theory of cellular toric varieties 细胞环状变的等变 $K$ 理论
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-22 DOI: arxiv-2404.14201
V. Uma
{"title":"Equivariant $K$-theory of cellular toric varieties","authors":"V. Uma","doi":"arxiv-2404.14201","DOIUrl":"https://doi.org/arxiv-2404.14201","url":null,"abstract":"In this article we describe the $T_{comp}$-equivariant topological $K$-ring of a $T$-{it cellular} simplicial toric variety. We further show that $K_{T_{comp}}^0(X)$ is isomorphic as an $R(T_{comp})$-algebra to the ring of piecewise Laurent polynomial functions on the associated fan denoted $PLP(Delta)$. Furthermore, we compute a basis for $K_{T_{comp}}^0(X)$ as a $R(T_{comp})$-module and multiplicative structure constants with respect to this basis.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798724","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
Equivariant Algebraic K-Theory and Derived completions III: Applications 等变代数 K 理论和衍生完备性 III：应用
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-19 DOI: arxiv-2404.13199
Gunnar Carlsson, Roy Joshua, Pablo Pelaez
{"title":"Equivariant Algebraic K-Theory and Derived completions III: Applications","authors":"Gunnar Carlsson, Roy Joshua, Pablo Pelaez","doi":"arxiv-2404.13199","DOIUrl":"https://doi.org/arxiv-2404.13199","url":null,"abstract":"In the present paper, we discuss applications of the derived completion\u0000theorems proven in our previous two papers. One of the main applications is to\u0000Riemann-Roch problems for forms of higher equivariant K-theory, which we are\u0000able to establish in great generality both for equivariant G-theory and\u0000equivariant homotopy K-theory with respect to actions of linear algebraic\u0000groups on normal quasi-projective schemes over a given field. We show such\u0000Riemann-Roch theorems apply to all toric and spherical varieties. We also obtain Lefschetz-Riemann-Roch theorems involving the fixed point\u0000schemes with respect to actions of diagonalizable group schemes. We also show\u0000the existence of certain spectral sequences that compute the homotopy groups of\u0000the derived completions of equivariant G-theory starting with equivariant\u0000Borel-Moore motivic cohomology.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806556","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
Equivariant Algebraic K-Theory and Derived completions II: the case of Equivariant Homotopy K-Theory and Equivariant K-Theory 等变代数 K 理论和衍生完备 II：等变同调 K 理论和等变 K 理论的情况
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-19 DOI: arxiv-2404.13196
Gunnar Carlsson, Roy Joshua, Pablo Pelaez
{"title":"Equivariant Algebraic K-Theory and Derived completions II: the case of Equivariant Homotopy K-Theory and Equivariant K-Theory","authors":"Gunnar Carlsson, Roy Joshua, Pablo Pelaez","doi":"arxiv-2404.13196","DOIUrl":"https://doi.org/arxiv-2404.13196","url":null,"abstract":"In the mid 1980s, while working on establishing completion theorems for\u0000equivariant Algebraic K-Theory similar to the well-known Atiyah-Segal\u0000completion theorem for equivariant topological K-theory, the late Robert\u0000Thomason found the strong finiteness conditions that are required in such\u0000theorems to be too restrictive. Then he made a conjecture on the existence of a\u0000completion theorem in the sense of Atiyah and Segal for equivariant Algebraic\u0000G-theory, for actions of linear algebraic groups on schemes that holds without\u0000any of the strong finiteness conditions that are required in such theorems\u0000proven by him, and also appearing in the original Atiyah-Segal theorem. In an\u0000earlier work by the first two authors, we solved this conjecture by providing a\u0000derived completion theorem for equivariant G-theory. In the present paper, we\u0000provide a similar derived completion theorem for the homotopy Algebraic\u0000K-theory of equivariant perfect complexes, on schemes that need not be regular. Our solution is broad enough to allow actions by all linear algebraic groups,\u0000irrespective of whether they are connected or not, and acting on any normal\u0000quasi-projective scheme of finite type over a field, irrespective of whether\u0000they are regular or projective. This allows us therefore to consider the\u0000Equivariant Homotopy Algebraic K-Theory of large classes of varieties like all\u0000toric varieties (for the action of a torus) and all spherical varieties (for\u0000the action of a reductive group). With finite coefficients invertible in the\u0000base fields, we are also able to obtain such derived completion theorems for\u0000equivariant algebraic K-theory but with respect to actions of diagonalizable\u0000group schemes. These enable us to obtain a wide range of applications, several\u0000of which are also explored.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140806655","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 relative homology criteria of smoothness 平稳性的相对同源性标准
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-12 DOI: arxiv-2404.08534
Kostiantyn Iusenko, Eduardo do Nascimento Marcos, Victor do Valle Pretti
{"title":"A relative homology criteria of smoothness","authors":"Kostiantyn Iusenko, Eduardo do Nascimento Marcos, Victor do Valle Pretti","doi":"arxiv-2404.08534","DOIUrl":"https://doi.org/arxiv-2404.08534","url":null,"abstract":"We investigate the relationship between smoothness and the relative global\u0000dimension. We prove that a smooth ring map $Bto A$ between commutative rings\u0000implies the finiteness of the relative global dimension\u0000$operatorname{gldim}(A,B)$. Conversely, we identify a sufficient condition on\u0000$B$ such that the finiteness of $operatorname{gldim}(A,B)$ implies the\u0000smoothness of the map $Bto A$.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"299 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140596759","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
Compactly supported $mathbb{A}^1$-Euler characteristics of symmetric powers of cellular varieties 细胞变体对称幂的紧凑支撑 $mathbb{A}^1$-Euler 特性
arXiv - MATH - K-Theory and Homology Pub Date : 2024-04-12 DOI: arxiv-2404.08486
Jesse Pajwani, Herman Rohrbach, Anna M. Viergever
{"title":"Compactly supported $mathbb{A}^1$-Euler characteristics of symmetric powers of cellular varieties","authors":"Jesse Pajwani, Herman Rohrbach, Anna M. Viergever","doi":"arxiv-2404.08486","DOIUrl":"https://doi.org/arxiv-2404.08486","url":null,"abstract":"The compactly supported $mathbb{A}^1$-Euler characteristic, introduced by\u0000Hoyois and later refined by Levine and others, is an anologue in motivic\u0000homotopy theory of the classical Euler characteristic of complex topological\u0000manifolds. It is an invariant on the Grothendieck ring of varieties\u0000$mathrm{K}_0(mathrm{Var}_k)$ taking values in the Grothendieck-Witt ring\u0000$mathrm{GW}(k)$ of the base field $k$. The former ring has a natural power\u0000structure induced by symmetric powers of varieties. In a recent preprint,\u0000Pajwani and P'al construct a power structure on $mathrm{GW}(k)$ and show that\u0000the compactly supported $mathbb{A}^1$-Euler characteristic respects these two\u0000power structures for $0$-dimensional varieties, or equivalently 'etale\u0000$k$-algebras. In this paper, we define the class $mathrm{Sym}_k$ of\u0000symmetrisable varieties to be those varieties for which the compactly supported\u0000$mathbb{A}^1$-Euler characteristic respects the power structures and study the\u0000algebraic properties of $mathrm{K}_0(mathrm{Sym}_k)$. We show that it\u0000includes all cellular varieties, and even linear varieties as introduced by\u0000Totaro. Moreover, we show that it includes non-linear varieties such as\u0000elliptic curves. As an application of our main result, we compute the compactly\u0000supported $mathbb{A}^1$-Euler characteristics of symmetric powers of\u0000Grassmannians and certain del Pezzo surfaces.","PeriodicalId":501143,"journal":{"name":"arXiv - MATH - K-Theory and Homology","volume":"239 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140564927","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