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The Hecke category is at the heart of several fundamental questions in modular representation theory. We emphasise the role of the "philosophy of deformations" both as a conceptual and computational tool, and suggest possible connections to…

Representation Theory · Mathematics 2020-01-15 Geordie Williamson

We extend the Bousfield-Kan spectral sequence for the computation of the homotopy groups of the space of minimal A-infinity algebra structures on a graded projective module. We use the new part to define obstructions to the extension of…

Algebraic Topology · Mathematics 2023-02-09 Fernando Muro

The Hom closed colocalizing subcategories of the stable module category of a finite group are classified. Along the way, the colocalizing subcategories of the homotopy category of injectives over an exterior algebra, and the derived…

Representation Theory · Mathematics 2011-02-15 Dave Benson , Srikanth B. Iyengar , Henning Krause

In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction…

Statistical Mechanics · Physics 2011-03-28 Ralph Kenna

Building on To\"en's work on affine stacks, we develop a certain homotopy theory for schemes, which we call "unipotent homotopy theory." Over a field of characteristic $p>0$, we prove that the unipotent homotopy group schemes…

Algebraic Geometry · Mathematics 2025-08-20 Shubhodip Mondal , Emanuel Reinecke

In this work we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously recovers a theorem of Stevenson when the list of elements is…

Commutative Algebra · Mathematics 2025-10-22 Jian Liu , Josh Pollitz

We give a construction of classifiers for double negation stable h-propositions in a variety of cubical set models of homotopy type theory and cubical type theory. This is used to give some relative consistency results: classifiers for…

Logic · Mathematics 2022-10-03 Andrew W. Swan

We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same…

Algebraic Topology · Mathematics 2020-03-09 Syunji Moriya

In this paper (a sequel to B. Drinovec Drnovsek and F. Forstneric, Holomorphic curves in complex spaces, Duke Math. J. 139 (2007), 203-253) we obtain existence and approximation results for closed complex subvarieties that are normalized by…

Complex Variables · Mathematics 2011-09-02 Barbara Drinovec Drnovsek , Franc Forstneric

For a profinite group $G$, let $(\text{-})^{hG}$, $(\text{-})^{h_dG}$, and $(\text{-})^{h'G}$ denote continuous homotopy fixed points for profinite $G$-spectra, discrete $G$-spectra, and continuous $G$-spectra (coming from towers of…

Algebraic Topology · Mathematics 2016-09-21 Daniel G. Davis , Gereon Quick

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…

Representation Theory · Mathematics 2017-06-14 Dave Benson , Srikanth B. Iyengar , Henning Krause , Julia Pevtsova

We study the holomorphic/meromorphic function theory and the fundamental group of Euclidean open neighborhoods of compact subvarieties in homogeneous spaces; building on results of Hironaka, Hartshorne, Napier and Ramachandran in the ample…

Algebraic Geometry · Mathematics 2013-08-27 János Kollár

This paper examines and strengthens the Cuntz-Thomsen picture of equivariant Kasparov theory for arbitrary second-countable locally compact groups, in which elements are given by certain pairs of cocycle representations between C*-dynamical…

Operator Algebras · Mathematics 2025-03-25 James Gabe , Gábor Szabó

Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi…

K-Theory and Homology · Mathematics 2012-09-05 Jan Essert

In this paper, we study the extent to which Bousfield and finite localizations relative to a thick subcategory of equivariant finite spectra preserve various kinds of highly structured multiplications. Along the way, we describe some basic,…

Algebraic Topology · Mathematics 2017-08-11 Michael A. Hill

We introduce a theory of stratifications of noncommutative stacks (i.e. presentable stable $\infty$-categories), and we prove a reconstruction theorem that expresses them in terms of their strata and gluing data. This reconstruction theorem…

Algebraic Geometry · Mathematics 2023-11-10 David Ayala , Aaron Mazel-Gee , Nick Rozenblyum

We develop a stable analogue to the theory of cosimplicial frames in model cagegories; this is used to enrich all homotopy categories of stable model categories over the usual stable homotopy category and to give a different description of…

Algebraic Topology · Mathematics 2010-02-16 Fabian Lenhardt

The purpose of this work is to study the notion of bivariant theory introduced by Fulton and MacPherson in the context of motivic stable homotopy theory, and more generally in the broader framework of Grothendieck six functors formalism. We…

Algebraic Geometry · Mathematics 2018-07-17 F. Déglise

A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…

Logic · Mathematics 2018-04-18 Daniel Palacín , Saharon Shelah

It is, by now, classical that lattices in higher rank semisimple groups have various rigidity properties. In this work, we add another such rigidity property to the list: uniform stability with respect to the family of unitary operators on…

Group Theory · Mathematics 2023-07-11 Lev Glebsky , Alexander Lubotzky , Nicolas Monod , Bharatram Rangarajan