Related papers: Differential Characters and $D$-Group Schemes

Let $X$ and $\mathfrak{a}$ be an affine scheme and (respectively) a finite-dimensional associative algebra over an algebraically-closed field $\Bbbk$, both equipped with actions by a linearly-reductive linear algebraic group $G$. We…

In the representation theory of reductive $p$-adic groups $G$, the issue of reducibility of induced representations is an issue of great intricacy. It is our contention, expressed as a conjecture in [3], that there exists a simple geometric…

Let X be a smooth projective curve over a field k of characteristic zero. The differential fundamental group of X is defined as the Tannakian dual to the category of vector bundles with (integrable) connections on X. This work investigates…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

Motivated by the study of meromorphic vector fields, a model theory of "compact complex manifolds equipped with a generic derivation" is here proposed. This is made precise by the notion of a differential CCM-structure. A first-order…

This paper is devoted to the study of the gluing construction for perverse sheaves on $G/U$ introduced by Kazhdan and Laumon ($G$ is a semisimple gourp, $U$ is the unipotent radical of a Borel subgroup in $G$). Kazhdan and Laumon…

The kernel relation $K$ on the lattice $\mathcal{L}(\mathcal{CR})$ of varieties of completely regular semigroups has been a central component in many investigations into the structure of $\mathcal{L}(\mathcal{CR})$. However, apart from the…

We investigate torsion elements in the kernel of the map on divisor class groups of excellent local normal domains A and A/I, for an ideal I of finite projective dimension. The motivation for this work is a result of Griffith-Weston which…

Consider a field k of characteristic p > 0, G_r the r-th Frobenius kernel of a smooth algebraic group G, DG_r the Drinfeld double of G_r, and M a finite dimensional DG_r-module. We prove that the cohomology algebra H*(DG_r,k) is finitely…

Let F be a finite field with q elements, let A be a finite dimensional F-algebra and let J=J(A) be the Jacobson radical of A. Then G=1+J is a p-group, where p is the characteristic of F. We refer to G as an F-algebra group. A subgroup H of…

Let M be a closed 3-manifold and S(M) the skein module of M at some odd root of unity. Using the Frobenius morphism, we can see S(M) as the space of global sections of a coherent sheaf over the SL2 character scheme of M. We prove that when…

We prove that the category of vector bundles over a fixed smooth manifold and its corresponding category of convenient modules are models for intuitionistic differential linear logic. The exponential modality is modelled by composing the…

Let $G$ be a finite group and let $k$ be a sufficiently large finite field. Let $R(G)$ denote the character ring of $G$ (i.e. the Grothendieck ring of the category of ${\mathbb{C}}G$-modules). We study the structure and the representations…

The notion of gluing of abelian categories was introduced by Kazhdan and Laumon in an attempt of another geometric construction of representations of finite Chevalley groups; the approach was later developed by Polishchuk and Braverman. We…

Let $k\subseteq K$ be a finite Galois extension of fields with Galois group $G$. Let $\mathscr{G}$ be the automorphism $k$-group scheme of $K$. We construct a canonical $k$-subgroup scheme $\underline{G}\subset\mathscr{G}$ with the property…

The classical radial part formula for the invariant differential operators and the K-invariant functions on a Riemannian symmetric space G/K is generalized to some non-invariant cases by use of Cherednik operators and a graded Hecke algebra…

It is well known that the set of isomorphism classes of extensions of groups with abelian kernel is characterized by the second cohomology group. In this paper we generalise this characterization of extensions to a natural class of…

Let $g$ be a semisimple Lie algebra over $\mathbb C$ and $k$ be a reductive in $g$ subalgebra. We say that a simple $g$-module $M$ is a $(g; k)$-module if as a $k$-module $M$ is a direct sum of finite-dimensional $k$-modules. We say that a…

Let $F$ be a global function field of characteristic $p>0$, $K/F$ an $\ell$-adic Lie extension ($\ell\neq p$) and $A/F$ an abelian variety. We provide Euler characteristic formulas for the $Gal(K/F)$-module $Sel_A(K)_\ell$.

Let $A$ be an abelian variety over the function field $K$ of a curve over a finite field. We describe several mild geometric conditions ensuring that the group $A(K^{\rm perf})$ is finitely generated and that the $p$-primary torsion…