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Triangulated categories of mixed motives

Cisinski, Denis-Charles.

Triangulated categories of mixed motives

Record Type:	Electronic resources : Monograph/item
Title/Author:	Triangulated categories of mixed motivesby Denis-Charles Cisinski, Frederic Deglise.
Author:	Cisinski, Denis-Charles.
other author:	Deglise, Frederic.
Published:	Cham :Springer International Publishing :2019.
Description:	xlii, 406 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Homotopy theory.
Online resource:	https://doi.org/10.1007/978-3-030-33242-6
ISBN:	9783030332426$q(electronic bk.)

Triangulated categories of mixed motives
Cisinski, Denis-Charles.

Triangulated categories of mixed motives[electronic resource] /by Denis-Charles Cisinski, Frederic Deglise. - Cham :Springer International Publishing :2019. - xlii, 406 p. :ill., digital ;24 cm. - Springer monographs in mathematics,1439-7382. - Springer monographs in mathematics..

Introduction -- Part I Fibred categories and the six functors formalism -- Part II Construction of fibred categories -- Part III Motivic complexes and relative cycles -- Part IV Beilinson motives and algebraic K-theory -- References -- Index -- Notation -- Index of properties of P-fibred triangulated categories.

The primary aim of this monograph is to achieve part of Beilinson's program on mixed motives using Voevodsky's theories of

ISBN: 9783030332426$q(electronic bk.)

Standard No.: 10.1007/978-3-030-33242-6doiSubjects--Topical Terms:

209299
Homotopy theory.

LC Class. No.: QA612.7 / .C57 2019

Dewey Class. No.: 514.24

Triangulated categories of mixed motives
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100 1 $a Cisinski, Denis-Charles. $3 855746
245 1 0 $a Triangulated categories of mixed motives $h [electronic resource] / $c by Denis-Charles Cisinski, Frederic Deglise.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xlii, 406 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 1439-7382
505 0 $a Introduction -- Part I Fibred categories and the six functors formalism -- Part II Construction of fibred categories -- Part III Motivic complexes and relative cycles -- Part IV Beilinson motives and algebraic K-theory -- References -- Index -- Notation -- Index of properties of P-fibred triangulated categories.
520 $a The primary aim of this monograph is to achieve part of Beilinson's program on mixed motives using Voevodsky's theories of $\ mathbb{A}^1 $- homotopy and motivic complexes. Historically, this book is the first to give a complete construction of a triangulated category of mixed motives with rational coefficients satisfying the full Grothendieck six functors formalism as well as fulfilling Beilinson's program, in particular the interpretation of rational higher Chow groups as extension groups. Apart from Voevodsky's entire work and Grothendieck's SGA4, our main sources are Gabber's work on etale cohomology and Ayoub's solution to Voevodsky's cross functors theory. We also thoroughly develop the theory of motivic complexes with integral coefficients over general bases, along the lines of Suslin and Voevodsky. Besides this achievement, this volume provides a complete toolkit for the study of systems of coefficients satisfying Grothendieck' six functors formalism, including Grothendieck-Verdier duality. It gives a systematic account of cohomological descent theory with an emphasis on h-descent. It formalizes morphisms of coefficient systems with a view towards realization functors and comparison results. The latter allows to understand the polymorphic nature of rational mixed motives. They can be characterized by one of the following properties: existence of transfers, universality of rational algebraic K-theory, h-descent, etale descent, orientation theory. This monograph is a longstanding research work of the two authors. The first three parts are written in a self-contained manner and could be accessible to graduate students with a background in algebraic geometry and homotopy theory. It is designed to be a reference work and could also be useful outside motivic homotopy theory. The last part, containing the most innovative results, assumes some knowledge of motivic homotopy theory, although precise statements and references are given.
650 0 $a Homotopy theory. $3 209299
650 0 $a Beilinson's conjectures. $3 855748
650 1 4 $a Algebraic Geometry. $3 274807
650 2 4 $a Category Theory, Homological Algebra. $3 275954
650 2 4 $a K-Theory. $3 277863
700 1 $a Deglise, Frederic. $3 855747
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Springer monographs in mathematics. $3 557774
856 4 0 $u https://doi.org/10.1007/978-3-030-33242-6
950 $a Mathematics and Statistics (Springer-11649)