Related papers: Tensor Abelian Geometry of VI-modules

One proves that each almost local-global semihereditary ring has the stacked basis property and is almost Bezout. If M is a finitely presented module, its torsion part tM is a direct sum of cyclic modules where the family of annhilators is…

Let $K$ be a field finitely generated over ${\Q}$, and $A$ an Abelian variety defined over $K$. Then by the Mordell-Weil Theorem, the set of rational points $A(K)$ is a finitely-generated Abelian group. In this paper, assuming Tate's…

We study the tensor-triangular geometry of the category of rational $G$-spectra for a compact Lie group $G$. In particular, we prove that this category can be naturally decomposed into local factors supported on individual subgroups, each…

Let E be a nonarchimedean local field with residue characteristic l, and suppose we have an n-dimensional representation of the absolute Galois group G_E of E over a reduced complete Noetherian local ring A with finite residue field k of…

We give a complete classification of the irreducible quasifinite modules for algebras of the form Vir \otimes A, where Vir is the Virasoro algebra and A is a Noetherian commutative associative unital algebra over the complex numbers. It is…

Given a suitable Noetherian scheme, we classify tensor $t$-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such $t$-structures restricting…

We study N\'eron models of pseudo-Abelian varieties over excellent discrete valuation rings of equal characteristic $p>0$ and generalize the notions of good reduction and semiabelian reduction to such algebraic groups. We prove that the…

We define a property for restricted Lie algebras in terms of cohomological support and tensor-triangular geometry of their categories of representations. By Tannakian reconstruction, the different symmetric tensor category structures on the…

The naive blow-up algebras developed by Keeler-Rogalski-Stafford, after examples of Rogalski, are the first known class of connected graded algebras that are noetherian but not strongly noetherian. This failure of the strong noetherian…

The present paper is devoted to an algebraic treatment of the joint spectral theory within the framework of Noetherian modules over an algebra finite extension of an algebraically closed field. We prove the spectral mapping theorem and…

We classify all irreducible generic $\mathrm{VI}$-modules in non-describing characteristic. Our result degenerates to yield a classification of irreducible generic $\mathrm{FI}$-modules in arbitrary characteristic. Our result can also be…

We study the representation theory of Dynkin quivers of type A in abstract stable homotopy theories, including those associated to fields, rings, schemes, differential-graded algebras, and ring spectra. Reflection functors, (partial)…

In recent years, researchers have discovered various large algebraic structures that have surprising finiteness properties, such as FI-modules and Delta-modules. In this paper, we add another example to the growing list: we show that…

It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is…

The purpose of this paper is to develop an efficient computational model for Abelian categories of coherent sheaves over certain classes of varieties. These categories are naturally described as Serre quotient categories. Hence, our…

We produce an integral model for the modular curve $X(Np^m)$ over the ring of integers of a sufficiently ramified extension of $\mathbf{Z}_p$ whose special fiber is a {\em semistable curve} in the sense that its only singularities are…

We consider a certain class of Schubert varieties of the affine Grassmannian of type A. By embedding a Schubert variety into a finite-dimensional Grassmannian, we construct an explicit basis of sections of the basic line bundle by…

Let k be an algebraically closed field of arbitrary characteristic,let K/k be a finitely generated field extension and let X be a separated scheme of finite type over K. For each prime ell, the absolute Galois group of K acts on the…

We prove that there exist some stacks, representable over the stack of stable curves, having the following universal property with respect to N\'eron models of Jacobians. For every one-parameter family of stable curves, with regular total…

This is a continuation of the paper "Modular tensor categories and orbifold theories", arXiv:math.QA/0104242. It discusses orbifold models of conformal filed theory, or, in mathematical language, question of constructing the category of…