Related papers: Characteristic-free approaches around Yu's constru…

We extend the results of Deligne and Illusie on liftings modulo $p^2$ and decompositions of the de Rham complex in several ways. We show that for a smooth scheme $X$ over a perfect field $k$ of characteristic $p>0$, the truncations of the…

In some recent work, Lusztig outlined a generalisation of the construction of Deligne and Lusztig to reductive groups over finite rings coming from the ring of integers in a local field, modulo some power of the maximal ideal. Lusztig…

We establish a formula for computing the unramified Brauer group of tame conic bundle threefolds in characteristic 2. The formula depends on the arrangement and residue double covers of the discriminant components, the latter being governed…

Let k be an algebraically closed field of characteristic p>0 and let G be a symplectic or general linear group over k. We consider induced modules for G under the assumption that p is bigger than the greatest hook length in the partitions…

Let X be a scheme of finite type over a Noetherian base scheme S admitting a dualizing complex, and let U be an open subset whose complement has codimension at least 2. We extend the Deligne-Bezrukavnikov theory of perverse coherent sheaves…

In this paper, we first study the lifting problem of Hasse-Schmidt derivations and then apply the results to the theory of locally trivial deformations of algebraic schemes in positive characteristic. As an application, we construct an…

Let $F/\mathbb{Q}$ be a totally real field and $A$ a modular $\GL_2$-type abelian variety over $F$. Let $K/F$ be a CM quadratic extension. Let $\chi$ be a class group character over $K$ such that the Rankin-Selberg convolution $L(s,A,\chi)$…

Let $G$ be a finitely generated torsion-free nilpotent group. The representation zeta function $\zeta_G(s)$ of $G$ enumerates twist isoclasses of finite-dimensional irreducible complex representations of $G$. We prove that $\zeta_G(s)$ has…

We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path…

We apply the technique of twisted extensions of infinite-dimensional Lie algebras to find new 3D integrable {\sc pde}s related to the deformations of Lie algebra $\mathbb{R}_N[s]\otimes \mathfrak{w}$ with $N=1, 2$ as well as to the Lie…

These are significantly expanded lecture notes for the author's minicourse at MSRI in June 2012, as published in the MSRI lecture note series, with some minor additional corrections. In these notes, we give an example-motivated review of…

Given a finite crystallographic root system $\Phi$ whose Dynkin diagram has a non-trivial automorphism, it yields a new root system $\Phi_{\tau}$ by a so-called classical folding. On the other hand, Lusztig's folding (1983) folds the root…

We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the analysis of a Leibniz algebra that underlies these vector…

This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations for the…

Let L/K be a finite Galois extension of complete local fields with finite residue fields and let G=Gal(L/K). Let G_1 and G_2 be the first and second ramification groups. Thus L/K is tamely ramified when G_1 is trivial and we say that L/K is…

In this paper, we prove several formulas related to Hodge theory, and using them to prove the deformations of a compact $H$-twisted generalized Calabi-Yau manifold are unobstructed and $L^2$ convergence in a neighborhood in another power…

We apply the filtered and graded methods developed in earlier works to find (noncommutative) free group algebras in division rings. If $L$ is a Lie algebra, we denote by $U(L)$ its universal enveloping algebra. P. M. Cohn constructed a…

This elementary discussion generalizes a Weyl geometry to allow quaternion valued gauge transformations and classical Yang-Mills geometric fields. This development will assume that the symmetric metric tensor is real in some gauge, and will…

The elliptic genera of two-dimensional N=2 superconformal field theories can be twisted by the action of the integral Heisenberg group if their U(1) charges are fractional. The basic properties of the resulting twisted elliptic genera and…

In this paper we apply a method devised in \cite{HartLarsSilv1D,LarsSilv1D} to the three-dimensional simple Lie algebra $\sll$. One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical…