Related papers: Krull-Schmidt decompositions for thick subcategori…

We introduce a notion of Milnor square of stable $\infty$-categories and prove a criterion under which algebraic K-theory sends such a square to a cartesian square of spectra. We apply this to prove Milnor excision and proper excision…

The paper gives a new proof that the model categories of stable modules for the rings Z/(p^2) and (Z/p)[\epsilon]/(\epsilon^2) are not Quillen equivalent. The proof uses homotopy endomorphism ring spectra. Our considerations lead to an…

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$. In this paper, we extend Hartshorne's characterization of cofinite complexes to more general classes of rings. We also determine conditions under which…

The classical HKR-theorem gives an isomorphism of the n-th Hochschild cohomology of a smooth algebra and the n-th exterior power of its module of K\"ahler differentials. Here we generalize it for simplicial, graded and anticommutative…

This paper studies the class group of graded integral domains. As an application, we state a decomposition theorem for class groups of semigroup rings. This recovers well-known results developed for the classic contexts of polynomial rings…

Let $\mathcal{D}(RC)$ be the derived category of representations of a small category $C$ over a commutative noetherian ring $R$. We study the homotopically smashing t-structures on this category. Specifying our discussion to the stalk…

We prove the decomposition theorem for Hodge modules with integral structure along proper K\"ahler morphisms, partially generalizing M. Saito's theorem for projective morphisms. Our proof relies on compactifications of period maps of…

We study rings of integral modular forms for congruence subgroups as modules over the ring of integral modular forms for the full modular group. In many cases these modules are free or decompose at least into well-understood pieces. We…

In this paper, we classify certain subcategories of modules over a ring R. A wide subcategory of R-modules is an Abelian subcategory of R-Mod that is closed under extensions. We give a complete classification of wide subcategories of…

In 2006, Restorff completed the classification of all Cuntz-Krieger algebras with finitely many ideals (i.e., those that are purely infinite) up to stable isomorphism. He left open the questions concerning strong classification up to stable…

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…

In this paper we study the indecomposable module categories over $\mathcal{C}(\mathfrak{sl}_N, k)$, the category of integrable level-$k$ respresentations of affine Kac-Moody $\mathfrak{sl}_N$. Our first main result classifies these module…

We define a topological Hochschild (THH) and cyclic (TC) homology theory for differential graded (dg) categories and construct several non-trivial natural transformations from algebraic K-theory to THH(-). In an intermediate step, we prove…

Let $\mathcal{E}=(\mathcal{A},\mathcal{S})$ be an exact category with enough projectives $\mathcal{P}$. We introduce the notion of support $\tau$-tilting subcategories of $\mathcal{E}$. It is compatible with existing definitions of support…

A kind of unstable homotopy theory on the category of associative rings (without unit) is developed. There are the notions of fibrations, homotopy (in the sense of Karoubi), path spaces, Puppe sequences, etc. One introduces the notion of a…

We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in…

Inspired by the classical category theorems of Halmos and Rohlin for the discrete measure preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C_0-semigroups on a separable Hilbert space.…

Combining results from Keller and Buchweitz, we describe the 1-periodic derived category of a finite dimensional algebra $A$ of finite global dimension as the stable category of maximal Cohen-Macaulay modules over some Gorenstein algebra…

Let G be a connected linear semisimple Lie group with Lie algebra g and maximal compact subgroup K. Let K_C -> Aut(p_C) be the complexified isotropy representation at the identity coset of the corresponding symmetric space. Suppose that O…