Related papers: Reduction theory for connections over the formal p…

The cutting equations are diagrammatic identities that are used to prove perturbative unitarity in quantum field theory. In this paper, we derive algebraic, upgraded versions of them. Differently from the diagrammatic versions, the…

We generalize Deligne's equivalence between the categories of regular-singular connections on the formal punctured disk and on the punctured affine line to the case where the base is a strictly Henselian discrete valuation ring of equal…

The aim of this paper is to give a proof of the restriction theorems for principal bundles with a reductive algebraic group as structure group in arbitrary characteristic. Let $G$ be a reductive algebraic group over any field $k=\bar{k}$,…

We provide a new condition for an absolutely almost simple algebraic group to have good reduction with respect to a discrete valuation of the base field which is formulated in terms of the existence of maximal tori with special properties.…

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing…

Among connected linear algebraic groups, quasi-reductive groups generalize pseudo-reductive groups, which in turn form a useful relaxation of the notion of reductivity. We study quasi-reductive groups over non-archimedean local fields,…

In the present paper, we prove the retract rationality of the classifying spaces $BG$ for several types of finite connected group schemes $G$ over algebraically closed fields of positive characteristic $p>0$. In particular, we prove the…

Let $A$ denote an affine algebra over an algebraically closed field $k$, with $\dim A=d\geq 3$. In the light of availability of cancellation theorems for stably free modules $P$ with $rank(P)=d-1$ (corank one), we try to implement the…

This is a survey article on some recent developments in the arithmetic theory of linear algebraic groups over higher-dimensional fields, written for the Notices of the AMS.

Let $G$ be a connected reductive algebraic group with simply connected derived subgroup. Over the complex numbers there exists a local method to study the geometric properties of a point $g$ in the closure of a Jordan class of $G$ in terms…

This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify…

Let $G$ be a connected complex Lie group. A real form of $G$ is a closed subgroup $H\subset G$ whose Lie algebra $\mathfrak{h}$ is a real form of the Lie algebra $\mathfrak{g}$ of $G$. A pair $(G,H)$ of this type is reductive, and the…

Partial connections are (singular) differential systems generalizing classical connections on principal bundles, yielding analogous decompositions for manifolds with nonfree group actions. Connection forms are interpreted as maps…

A full Lie point symmetry analysis of rational difference equations is performed. Non-trivial symmetries are derived and exact solutions using these symmetries are obtained.

This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and, then, we extend it to the nonlinear setting…

We prove several basic extension theorems for reductive group schemes. We also prove that each Lie algebra with a perfect Killing form over a commutative $\dbZ$-algebra, is the Lie algebra of an adjoint group scheme.

We define the stack of $G$-local systems with restricted variation on the formal puntured disc and study its properties. We embed sheaves of categories over this stack into the category of factorization module categories over…

We prove a semistable reduction theorem for principal bundles on curves in almost arbitrary characteristics. For exceptional groups we need some small explicit restrictions on the characteristic.

Let G be a connected reductive linear algebraic group. The aim of this note is to settle a question of J-P. Serre concerning the behaviour of his notion of G-complete reducibility under separable field extensions. Part of our proof relies…

Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…