Extended abstracts Spring 2015 : interactions between representation theory, algebraic topology and commutative algebra

✍ Scribed by Herbera, Dolors; Pitsch, Wolfgang; Zarzuela, Santiago

• Publisher: Birkhäuser
• Year: 2016
• Tongue: English
• Leaves: 180
• Series: Trends in mathematics. Research perspectives CRM Barcelona ; volume 5
• Category: Library

✦ Synopsis

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. Read more...

Abstract: 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

✦ Table of Contents

Front Matter ....Pages i-ix
Homological Algebra on an Adams Algebraic Stack (Leovigildo Alonso Tarrío)....Pages 1-5
Lyubeznik Numbers of Local Rings and Linear Strands of Graded Ideals (Josep Àlvarez Montaner)....Pages 7-13
The Heart of a t-Structure Induced by a n-Tilting Module (Silvana Bazzoni)....Pages 15-19
On Some Local Cohomology Spectral Sequences (Alberto F. Boix)....Pages 21-26
Homotopy Representations of Classifying Spaces (Natàlia Castellana)....Pages 27-33
Decomposing Gorenstein Rings as Connected Sums (Hariharan Ananthnarayan, Ela Celikbas, Zheng Yang)....Pages 35-39
Rigid and Test Modules (Olgur Celikbas)....Pages 41-46
Tate Homology Beyond Gorenstein Rings (Lars Winther Christensen)....Pages 47-51
On the Classification of Artin Algebras and the Inverse System of Macaulay (Joan Elias)....Pages 53-57
Purity in Categories of Sheaves (Sergio Estrada)....Pages 59-62
Idempotent Functors and Nilpotent Spaces (Wojciech Chachólski, Emmanuel Dror Farjoun, Ramón Flores, Jérôme Scherer)....Pages 63-67
Decomposition Spaces and Incidence (Co)Algebras (Imma Gálvez-Carrillo)....Pages 69-74
Cellular Approximations for Fusion Systems (Alberto Gavira-Romero)....Pages 75-80
Homological Epimorphisms and the Lie Bracket in Hochschild Cohomology (Reiner Hermann)....Pages 81-85
Gorenstein Projective Precovers (Alina Iacob)....Pages 87-90
Hochschild Homology on Schemes and Fundamental Class (Ana Jeremías López)....Pages 91-95
A Remark on Leclerc’s Frobenius Categories (Martin Kalck)....Pages 97-101
Atom-Molecule Correspondence in Grothendieck Categories (Ryo Kanda)....Pages 103-107
Proalgebraic Crossed Modules of Quasirational Presentations (Andrey Mikhovich)....Pages 109-114
Some F-Invariants for Quotient Singularities (Yusuke Nakajima)....Pages 115-119
Strong Generation of Some Derived Categories of Schemes (Amnon Neeman)....Pages 121-127
Regularity of Products over Quadratic Hypersurfaces (Hop D. Nguyen, Thanh Vu)....Pages 129-132
Phantom Maps and Representability (Oriol Raventós)....Pages 133-136
Six Operations on dg Enhancements of Derived Categories of Sheaves and Applications (Olaf M. Schnürer)....Pages 137-141
Tensor Product of Dualizing Complexes over a Field (Liran Shaul)....Pages 143-147
Strong Generators in Tensor Triangulated Categories (Johan Steen)....Pages 149-153
Abelian Model Structures and Applications (Jan Šťovíček)....Pages 155-159
Singularity Categories of Stable Resolving Subcategories and Applications to Gorenstein Rings (Ryo Takahashi)....Pages 161-165
Classes of Flat Modules Arising in Algebraic Geometry and Approximations (Jan Trlifaj)....Pages 167-171
The Dual Graph of an Arithmetically Gorenstein Scheme (Matteo Varbaro)....Pages 173-174
Baez–Dolan Stabilization via (Semi-)Model Categories of Operads (David White, Michael Batanin)....Pages 175-179
Vanishing of Tor (Olgur Celikbas, Roger Wiegand)....Pages 181-185
Prime Ideals in Noetherian Rings (Sylvia Wiegand)....Pages 187-192

✦ Subjects

Representations of algebras;Algebraic topology;Commutative algebra;MATHEMATICS -- Algebra -- Intermediate