東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Lectures on functor homology

Franjou, Vincent.

FindBook

Google Book

Amazon

博客來

Lectures on functor homology

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Lectures on functor homology/ edited by Vincent Franjou, Antoine Touze.
其他作者:	Franjou, Vincent.
出版者:	Cham :Springer International Publishing : : 2015.,
面頁冊數:	vi, 149 p. :ill. (some col.), digital ;24 cm.
內容註:	Introduction -- A. Djament: Homologie stable des groupes a coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touze: Prerequisites of Homological Algebra.
Contained By:	Springer eBooks
標題:	Functor theory. -
電子資源:	http://dx.doi.org/10.1007/978-3-319-21305-7
ISBN:	9783319213057$q(electronic bk.)

Lectures on functor homology
Lectures on functor homology[electronic resource] /edited by Vincent Franjou, Antoine Touze. - Cham :Springer International Publishing :2015. - vi, 149 p. :ill. (some col.), digital ;24 cm. - Progress in mathematics,v.3110743-1643 ;. - Progress in mathematics ;v.295..

Introduction -- A. Djament: Homologie stable des groupes a coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touze: Prerequisites of Homological Algebra.

This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurelien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament's theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko's unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert's fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin's strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov's lectures highlight topological invariants: homotopy and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touze's introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.

ISBN: 9783319213057$q(electronic bk.)

Standard No.: 10.1007/978-3-319-21305-7doiSubjects--Topical Terms:

735159
Functor theory.

LC Class. No.: QA169

Dewey Class. No.: 515.7

Lectures on functor homology
LDR:03276nmm a2200337 a 4500 001 2016498
003 DE-He213
005 20160512144031.0
006 m d
007 cr nn 008maaau
008 160613s2015 gw s 0 eng d
020 $a 9783319213057$q(electronic bk.)
020 $a 9783319213040$q(paper)
024 7 $a 10.1007/978-3-319-21305-7 $2 doi
035 $a 978-3-319-21305-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA169
072 7 $a PBC $2 bicssc
072 7 $a PBF $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 515.7 $2 23
090 $a QA169 $b .L471 2015
245 0 0 $a Lectures on functor homology $h [electronic resource] / $c edited by Vincent Franjou, Antoine Touze.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2015.
300 $a vi, 149 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Progress in mathematics, $x 0743-1643 ; $v v.311
505 0 $a Introduction -- A. Djament: Homologie stable des groupes a coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touze: Prerequisites of Homological Algebra.
520 $a This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both essential insights and new methods for tackling difficult mathematical problems. In the lectures by Aurelien Djament, polynomial functors appear as coefficients in the homology of infinite families of classical groups, e.g. general linear groups or symplectic groups, and their stabilization. Djament's theorem states that this stable homology can be computed using only the homology with trivial coefficients and the manageable functor homology. The series includes an intriguing development of Scorichenko's unpublished results. The lectures by Wilberd van der Kallen lead to the solution of the general cohomological finite generation problem, extending Hilbert's fourteenth problem and its solution to the context of cohomology. The focus here is on the cohomology of algebraic groups, or rational cohomology, and the coefficients are Friedlander and Suslin's strict polynomial functors, a conceptual form of modules over the Schur algebra. Roman Mikhailov's lectures highlight topological invariants: homotopy and homology of topological spaces, through derived functors of polynomial functors. In this regard the functor framework makes better use of naturality, allowing it to reach calculations that remain beyond the grasp of classical algebraic topology. Lastly, Antoine Touze's introductory course on homological algebra makes the book accessible to graduate students new to the field. The links between functor homology and the three fields mentioned above offer compelling arguments for pushing the development of the functor viewpoint. The lectures in this book will provide readers with a feel for functors, and a valuable new perspective to apply to their favourite problems.
650 0 $a Functor theory. $3 735159
650 0 $a Homology theory. $3 555733
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Group Theory and Generalizations. $3 893889
650 2 4 $a Algebraic Topology. $3 891269
700 1 $a Franjou, Vincent. $3 2165616
700 1 $a Touze, Antoine. $3 2165617
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a Progress in mathematics ; $v v.295. $3 1566157
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-21305-7
950 $a Mathematics and Statistics (Springer-11649)