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 Ph D and postdoctoral students who want to learn more about the latest advances in these highly active fields of research.
Содержание
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.
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