Pub Date : 2013-08-01DOI: 10.1017/IS013004029JKT226
P. Baum, A. Carey, Bai-Ling Wang
{"title":"K-cycles for twisted K-homology","authors":"P. Baum, A. Carey, Bai-Ling Wang","doi":"10.1017/IS013004029JKT226","DOIUrl":"https://doi.org/10.1017/IS013004029JKT226","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"12 1","pages":"69-98"},"PeriodicalIF":0.0,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS013004029JKT226","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668019","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 : 2013-08-01DOI: 10.1017/IS013005020JKT230
F. Keune
{"title":"Relative reciprocities on Dedekind domains","authors":"F. Keune","doi":"10.1017/IS013005020JKT230","DOIUrl":"https://doi.org/10.1017/IS013005020JKT230","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"12 1","pages":"125-136"},"PeriodicalIF":0.0,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS013005020JKT230","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668031","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 : 2013-08-01DOI: 10.1017/IS013005031JKT227
M. Kolster, A. Movahhedi
For an odd prime p we prove a Riemann-Hurwitz type formula for odd eigenspaces of the standard Iwasawa modules over F ( μ p ∞), the field obtained from a totally real number field F by adjoining all p -power roots of unity. We use a new approach based on the relationship between eigenspaces and etale cohomology groups over the cyclotomic ℤ p -extension F ∞ of F . The systematic use of etale cohomology greatly simplifies the proof and allows to generalize the classical result about the minus-eigenspace to all odd eigenspaces.
{"title":"On λ-invariants of number fields and étale cohomology","authors":"M. Kolster, A. Movahhedi","doi":"10.1017/IS013005031JKT227","DOIUrl":"https://doi.org/10.1017/IS013005031JKT227","url":null,"abstract":"For an odd prime p we prove a Riemann-Hurwitz type formula for odd eigenspaces of the standard Iwasawa modules over F ( μ p ∞), the field obtained from a totally real number field F by adjoining all p -power roots of unity. We use a new approach based on the relationship between eigenspaces and etale cohomology groups over the cyclotomic ℤ p -extension F ∞ of F . The systematic use of etale cohomology greatly simplifies the proof and allows to generalize the classical result about the minus-eigenspace to all odd eigenspaces.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"12 1","pages":"167-181"},"PeriodicalIF":0.0,"publicationDate":"2013-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS013005031JKT227","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56668042","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 : 2013-06-01DOI: 10.1017/IS011001005JKT209
D. Ravenel
In 1969 Quillen discovered a deep connection between complex cobordism and formal group laws which he announced in [Qui69]. Algebraic topology has never been the same since. We will describe the content of [Qui69] and then discuss its impact on the field. This paper is a writeup of a talk on the same topic given at the Quillen Conference at MIT in October 2012. Slides for that talk are available on the author's home page.
{"title":"Quillen's work on formal group laws and complex cobordism theory","authors":"D. Ravenel","doi":"10.1017/IS011001005JKT209","DOIUrl":"https://doi.org/10.1017/IS011001005JKT209","url":null,"abstract":"In 1969 Quillen discovered a deep connection between complex cobordism and formal group laws which he announced in [Qui69]. Algebraic topology has never been the same since. We will describe the content of [Qui69] and then discuss its impact on the field. This paper is a writeup of a talk on the same topic given at the Quillen Conference at MIT in October 2012. Slides for that talk are available on the author's home page.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"493-506"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011001005JKT209","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56665906","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 : 2013-06-01DOI: 10.1017/IS012011006JKT202
J. Brodzki
The excision theorem of Cuntz and Quillen established the existence of a six term exact sequence in the bivariant periodic cyclic cohomology HP*(–,–) associated with an arbitrary algebra extension 0 ? S ? P ? Q ? 0. This remarkable result enabled far reaching developments in the purely algebraic periodic cyclic cohomology. It also provided a new formalism that led to the creation of new versions of this theory for topological and bornological algebras. In this article we outline some of the developments that resulted from this breakthrough.
{"title":"Cyclic cohomology after the excision theorem of Cuntz and Quillen","authors":"J. Brodzki","doi":"10.1017/IS012011006JKT202","DOIUrl":"https://doi.org/10.1017/IS012011006JKT202","url":null,"abstract":"The excision theorem of Cuntz and Quillen established the existence of a six term exact sequence in the bivariant periodic cyclic cohomology HP*(–,–) associated with an arbitrary algebra extension 0 ? S ? P ? Q ? 0. This remarkable result enabled far reaching developments in the purely algebraic periodic cyclic cohomology. It also provided a new formalism that led to the creation of new versions of this theory for topological and bornological algebras. In this article we outline some of the developments that resulted from this breakthrough.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"575-598"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012011006JKT202","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666846","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 : 2013-06-01DOI: 10.1017/IS011012012JKT207
W. Dwyer
In the 1960's and 1970's, the Adams Conjecture g- ured prominently both in homotopy theory and in geometric topol- ogy. Quillen sketched one way to attack the conjecture and then proved it with an entirely dierent line of argument. Both of his approaches led to spectacular and beautiful new mathematics. 1. Background on the Adams Conjecture For a nite CW -complex X, let KO(X) be the Grothendieck group of nite-dimensional real vector bundles over X, and J(X) the quo- tient of KO(X) by the subgroup generated by dierences , where and are vector bundles whose associated sphere bundles are
{"title":"QUILLEN'S WORK ON THE ADAMS CONJECTURE","authors":"W. Dwyer","doi":"10.1017/IS011012012JKT207","DOIUrl":"https://doi.org/10.1017/IS011012012JKT207","url":null,"abstract":"In the 1960's and 1970's, the Adams Conjecture g- ured prominently both in homotopy theory and in geometric topol- ogy. Quillen sketched one way to attack the conjecture and then proved it with an entirely dierent line of argument. Both of his approaches led to spectacular and beautiful new mathematics. 1. Background on the Adams Conjecture For a nite CW -complex X, let KO(X) be the Grothendieck group of nite-dimensional real vector bundles over X, and J(X) the quo- tient of KO(X) by the subgroup generated by dierences , where and are vector bundles whose associated sphere bundles are","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"517-526"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011012012JKT207","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666771","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 : 2013-06-01DOI: 10.1017/IS012011011JKT203
Daniel R. Grayson
We survey the genesis and development of higher algebraic K-theory by Daniel Quillen.
我们考察了Daniel Quillen的高等代数k理论的起源和发展。
{"title":"Quillen's work in algebraic K -theory","authors":"Daniel R. Grayson","doi":"10.1017/IS012011011JKT203","DOIUrl":"https://doi.org/10.1017/IS012011011JKT203","url":null,"abstract":"We survey the genesis and development of higher algebraic K-theory by Daniel Quillen.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"527-547"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS012011011JKT203","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56666851","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 : 2013-06-01DOI: 10.1017/IS013007022JKT238
A. Bak, Jonathan Rosenberg, C. Weibel
{"title":"The Legacy of Daniel Quillen","authors":"A. Bak, Jonathan Rosenberg, C. Weibel","doi":"10.1017/IS013007022JKT238","DOIUrl":"https://doi.org/10.1017/IS013007022JKT238","url":null,"abstract":"","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"465-467"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS013007022JKT238","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56667590","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 : 2013-06-01DOI: 10.1017/IS013001006JKT204
Jean-Claude Thomas, Micheline Vigué-Poirrier
In this short paper we try to describe the fundamental contribution of Q uillen in the development of abstract homotopy theory and we explain how he uses this theory to lay the foundations of rational homotopy theory.
{"title":"Daniel Quillen, the father of abstract homotopy theory","authors":"Jean-Claude Thomas, Micheline Vigué-Poirrier","doi":"10.1017/IS013001006JKT204","DOIUrl":"https://doi.org/10.1017/IS013001006JKT204","url":null,"abstract":"In this short paper we try to describe the fundamental contribution of Q uillen in the development of abstract homotopy theory and we explain how he uses this theory to lay the foundations of rational homotopy theory.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"11 1","pages":"479-491"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS013001006JKT204","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"56667267","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 : 2013-06-01DOI: 10.1017/IS011012012JKT208
Mark Hovey
We provide a brief description of the mathematics that led to Daniel Quillen’s introduction of model categories, a summary of his seminal work “Homotopical algebra”, and a brief description of some of the developments in the field since.
{"title":"Quillen model categories","authors":"Mark Hovey","doi":"10.1017/IS011012012JKT208","DOIUrl":"https://doi.org/10.1017/IS011012012JKT208","url":null,"abstract":"We provide a brief description of the mathematics that led to Daniel Quillen’s introduction of model categories, a summary of his seminal work “Homotopical algebra”, and a brief description of some of the developments in the field since.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"13 1","pages":"469-478"},"PeriodicalIF":0.0,"publicationDate":"2013-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78542758","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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