Extended Abstracts Spring 2015 : Interactions between Representation Theory, Algebraic Topology and Commutative Algebra / edited by Dolors Herbera, Wolfgang Pitsch, Santiago Zarzuela.

Format:

Book

Contributor:

Herbera, Dolors., Editor.

Pitsch, Wolfgang., Editor.

Zarzuela, Santiago., Editor.

Series:

Research Perspectives CRM Barcelona, 2509-7415 ; 5

Language:

English

Subjects (All):

Commutative algebra.

Commutative rings.

Commutative Rings and Algebras.

Local Subjects:

Commutative Rings and Algebras.

Physical Description:

1 online resource (IX, 192 p. 2 illus.)

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.

Summary:

This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest developments in the area. It appeals to established researchers as well as PhD and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.

Contents:

Homological Algebra on an Adams Algebraic Stack

Lyubeznik Numbers of Local Rings and Linear Strands of Graded Ideals

The Heart of a t-Structure Induced by a n-Tilting Module

On Some Local Cohomology Spectral Sequences

Homotopy Representations of Classifying Spaces

Decomposing Gorenstein Rings as Connected Sums

Rigid and Test Modules

Tate Homology Beyond Gorenstein Rings

On the Classication of Artin Algebras and the Inverse System of Macaulay

Purity in Categories of Sheaves

Idempotent Functors and Nilpotent Spaces

Decomposition Spaces and Incidence (Co)Algebras

Cellular Approximations for Fusion Systems

Homological Epimorphisms and the Lie Bracket in Hochschild Cohomology

Gorenstein Projective Precovers

Hochschild Homology on Schemes and Fundamental Class

A Remark on Leclerc's Frobenius Categories

Atom-Molecule Correspondencein Grothendieck Categories

Proalgebraic Crossed Modules of Quasirational Presentations

Some F-Invariants for Quotient Singularities

Strong Generation of Some Derived Categories of Schemes

Regularity of Products over Quadratic Hypersurfaces

Phantom Maps and Representability

Six Operations on dg Enhancements of Derived Categories of Sheaves and Applications

Tensor Product of Dualizing Complexes over a Field

Strong Generators in Tensor Triangulated Categories

Abelian Model Structures and Applications

Singularity Categories of Stable Resolving Subcategories and Applications to Gorenstein Rings

Classes of Flat Modules Arising in Algebraic Geometry and Approximations

The Dual Graph of an Arithmetically Gorenstein Scheme

Baez-Dolan Stabilization via (Semi-)Model Categories of Operads

Vanishing of Tor

Prime Ideals in Noetherian Rings.

Notes:

Includes bibliographical references.