Related papers: Projectivity of modules for infinitesimal unipoten…

We study irreducible restrictions from modules over symmetric groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. Such results are known when the…

Let $G= SL_{n+1}$ be defined over an algebraically closed field of characteristic $p > 2$. For each $n \geq 1$ there exists a singular block in the category of $G_1$-modules which contains precisely $n+1$ irreducible modules. We are…

In an earlier paper we showed that we can improve results by Emmy Noether and Alexander Ostrowski concerning the reducibility modulo p of absolutely irreducible polynomials with integer coefficients by giving the problem a geometric turn…

We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…

Consider a finite group $G$ acting on a graded Noetherian $k$-algebra $S$, for some field $k$ of characteristic $p$; for example $S$ might be a polynomial ring. Regard $S$ as a $kG$-module and consider the multiplicity of a particular…

We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.

We give an easy proof of Sch\"utzenberger's Theorem stating that non-commutative formal power series are rational if and only if they are recognisable. A byproduct of this proof is a natural metric on a subgroup of invertible rational…

We prove that certain modules are faithful. This enables us to draw consequences about the reduction number and the integral closure of some classes of ideals.

We prove various finiteness and representability results for cohomology of finite flat abelian group schemes. In particular, we show that if $f\colon X\rightarrow \mathrm{Spec}(k)$ is a projective scheme over a field $k$ and $G$ is a finite…

We give a classification of all irreducible completely pointed $U_q(\mathfrak{sl}_{n+1})$ modules over a characteristic zero field in which $q$ is not a root of unity. This generalizes the classification result of Benkart, Britten and…

We construct examples of bounded below, noncontractible, acyclic complexes of finitely generated projective modules over some rings $S$, as well as bounded above, noncontractible, acyclic complexes of injective modules. The rings $S$ are…

Let D be a connected component of a reductive group over an algebraically closed field. We define a surjective map from the unipotent character sheaves on D to the set of strata of D, extending an earlier result which applied to connected…

We prove that the theory of all modules over the ring of algebraic integers is decidable.

Let $R$ be a commutative ring. We show that pure injective resolutions and pure projective resolutions can be constructed for unbounded complexes of $R$-modules. We use these to obtain a closed symmetric monoidal structure on the unbounded…

We explicitly construct the structure of Jacquet modules of parabolically induced representations of even unitary groups and even general unitary groups over a $p$-adic field $F$ of characteristic different than two. As an application, we…

We prove that any smooth rational projective surface over the field of complex numbers has an open covering consisting of 3 subsets isomorphic to affine planes.

In this paper we construct the moduli of semistable principal bundles with structure group a semisimple group, over nonsingular curves in positive characteristic, with good bounds on the prime.

We describe rings over which every right module is almost injective. We give a description of rings over which every simple module is a almost projective.

We show that an A-infinity algebra structure can be transferred to a projective resolution of the complex underlying any A-infinity algebra. Under certain connectedness assumptions, this transferred structure is unique up to homotopy. In…

We undertake a study of extensions of unirational algebraic groups. We prove that extensions of unirational groups are also unirational over fields of degree of imperfection $1$, but that this fails over every field of higher degree of…