Related papers: Singularities of Steinberg deformation rings

Let $p:X \rightarrow S$ be a flat, proper and regular scheme over a strictly henselian discrete valuation ring. We prove that the singularity category of the special fiber with its natural two-periodic structure allows to recover the…

Let $(R, \mathfrak{m}, k)$ denote a local Cohen-Macaulay ring such that the category of maximal Cohen-Macaulay $R$-modules $\textbf{mcm}\ R$ contains an $n$-cluster tilting object $L$. In this paper, we compute $G_1(R) := K_1(\textbf{mod}\…

We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of $\GL_2$ over an algebraically closed field of characteristic $p>2$, that is, of any block whose number of simple modules is a power of…

We introduce certain quiver analogue of the determinantal variety. We study the Kempf-Lascoux-Weyman's complex associated to a line bundle on the variety. In the case of generalized Kronecker quivers, we give a sufficient condition on when…

We prove a statement of Ax-Lindemann type for the uniformization of products of Mumford curves whose associated fundamental groups are non-abelian Schottky subgroups of $\mathop{\rm PGL}(2,\bar{\mathbf Q_p})$ contained in $\mathop{\rm…

Let $R$ be a unital ring satisfying the invariant basis number property, that every stably free $R$-module is free, and that the complex of partial bases of every finite rank free module is Cohen--Macaulay. This class of rings includes…

Let W be a finite irreducible Coxeter group and let X_W be the classifying space for G_W, the associated Artin group. If A is a commutative unitary ring, we consider the two local systems L_q and L_q' over X_W, respectively over the modules…

We begin the systematic study of cohomological Hecke operators of modifications of coherent sheaves on a smooth surface $X$, along a fixed proper curve $Z \subset X$. We develop the necessary geometric foundations in order to define the…

In this paper, we consider a connected Riemannian manifold $M$ where a connected Lie group $G$ acts effectively and isometrically. Assume $X\in\mathfrak{g}=\mathrm{Lie}(G)$ defines a bounded Killing vector field, we find some crucial…

We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components…

Let G be a complex semi-simple group, X a Riemann surface, M_G the moduli space of principal G-bundles on X. When G is simply-connected, there exists a closed formula expressing the dimension of the space H^0(M_G,L) for any line bundle L on…

We prove a version of quantum geometric Langlands conjecture in characteristic $p$. Namely, we construct an equivalence of certain localizations of derived categories of twisted crystalline $\mathcal D$-modules on the stack of rank $N$…

Let $R$ be an excellent Henselian discrete valuation ring with algebraically closed residue field $k$ of any characteristic. Fix integers $r,d$ with $r\ge 2$. Let $X_R$ be a regular fibred surface over Spec($R$) with special fibre denoted…

Given a compact Riemann surface $X$ of genus at least $2$ with automorphism group $G$ we provide formulae that enable us to compute traces of automorphisms of X on the space of global sections of $G$-linearized line bundles defined on…

For a complex reductive Lie algebra $\mathfrak{g}$ with Cartan subalgebra $\mathfrak{h}$ and Weyl group $W$ we consider the category $\text{Perv}(W \backslash \mathfrak{h})$ of perverse sheaves on $W \backslash \mathfrak{h}$ smooth w.r.t.…

Over a field of characteristic 0, every ring of invariants of a finite group is Cohen-Macaulay. This is not true for fields of positive characteristic. We consider permutation representations and their invariant rings over fields…

In this article, we derive estimates of Teichm\"uller modular forms, and associated invariants. Let $\mathcal{M}_{g}$ denote the moduli space of compact hyperbolic Riemann surfaces of genus $g\geq 2$, and let $\overline{M}_{g}$ be the…

Let G be a connected reductive complex affine algebraic group, and let X denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in X, extending a theorem of Richardson and proving…

This is the second in a series of five papers math.DG/0211294, math.DG/0302355, math.DG/0302356, math.DG/0303272 studying special Lagrangian submanifolds (SL m-folds) X in (almost) Calabi-Yau m-folds M with singularities x_1,...,x_n locally…

Let $k$ be a field of odd prime characteristic $p$. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over $k$. As a consequence, we prove that if $B$ is a defect…