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Lectures on functor homology [electronic resource]

Lectures on functor homology [electronic resource]

자료유형
E-Book(소장)
개인저자
Franjou, Vincent. Touzé, Antoine.
서명 / 저자사항
Lectures on functor homology [electronic resource] / Vincent Franjou, Antoine Touzé, editors.
발행사항
Cham :   Springer International Publishing :   Imprint: Springer,   2015.  
형태사항
1 online resource (vi, 149 p.) : ill. (some col.).
총서사항
Progress in mathematics,0743-1643 ; 311
ISBN
9783319213057
요약
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 Aurélien 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 The series includes an intriguing development of Scorichenko’s unpublished results.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 Touzé’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.
일반주기
Title from e-Book title page.  
내용주기
Introduction -- A. Djament: Homologie stable des groupes à coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touzé: Prerequisites of Homological Algebra.
서지주기
Includes bibliographical references.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Functor theory.
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020 ▼a 9783319213057
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082 0 4 ▼a 512.64 ▼2 23
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245 0 0 ▼a Lectures on functor homology ▼h [electronic resource] / ▼c Vincent Franjou, Antoine Touzé, editors.
260 ▼a Cham : ▼b Springer International Publishing : ▼b Imprint: Springer, ▼c 2015.
300 ▼a 1 online resource (vi, 149 p.) : ▼b ill. (some col.).
490 1 ▼a Progress in mathematics, ▼x 0743-1643 ; ▼v 311
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references.
505 0 ▼a Introduction -- A. Djament: Homologie stable des groupes à coefficients polynomiaux -- W. van der Kallen: Lectures on Bifunctors and Finite Generation of Rational Cohomology Algebras -- R. Mikhailov: Polynomial Functors and Homotopy Theory -- A. Touzé: 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 Aurélien 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 Touzé’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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Functor theory.
700 1 ▼a Franjou, Vincent.
700 1 ▼a Touzé, Antoine.
830 0 ▼a Progress in mathematics ; ▼v 311.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-319-21305-7
945 ▼a KLPA
991 ▼a E-Book(소장)

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