Related papers: A higher-dimensional Chevalley restriction theorem…

We give a criterion of integrality of an one-dimensional formal group law in terms of congruences satisfied by the coefficients of the canonical invariant differential. For an integral formal group law a p-adic analytic formula for the…

The goal of this paper is to establish a general rigidity statement for abstract representations of elementary subgroups of Chevalley groups of rank at least 2 over a class of commutative rings that includes the localizations of 1-generated…

We give a short proof of Chevalley's theorem that every algebraic group is an extension of an Abelian variety by a linear algebraic group. Along the way we treat Bertini's irreducibility theorem.

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and then we obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace…

Given a Chevalley group ${\mathbf G}(q)$ and a parabolic subgroup $P\subset {\mathbf G}(q)$, we prove that for any set $A$ there is a certain growth of $A$ relatively to $P$, namely, either $AP$ or $PA$ is much larger than $A$. Also, we…

We show that elementary amenable groups, which have a bound on the orders of their finite subgroups, admit a finite dimensional model for the classifying space with virtually cyclic isotropy.

The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic. The purpose of this…

M. R. R. Moghaddam (Monatsh. Math. 90 (1980) 37-43.) showed that the Baer invariant commutes with the direct limit of a directed system of groups. In this paper, using the generalization of Schur's formula for the structure of a…

Classical Hamiltonian system of a point moving on a sphere of fixed radius is shown to emerge from the constrained evolution of quantum spin. The constrained quantum evolution corresponds to an appropriate coarse-graining of the quantum…

We prove a strengthening of the Grothendieck-Lefschetz hyperplane theorem for local Picard groups conjectured by Koll\'ar. Our approach, which relies on acyclicity results for absolute integral closures, also leads to a restriction theorem…

We define the notion of a sheaf over a complex of groups. As an application, we give a criterion for the developability of a complex of groups. When the developability is witnessed by a morphism to $\mathrm{GL}(V)$ for some $V$, our…

A classical theorem of Paley asserts the existence of an infinite family of quadratic characters whose character sums become exceptionally large. In this paper, we establish an analogous result for characters of any fixed even order.…

We prove moving lemma for additive higher Chow groups of smooth projective varieties. As applications, we prove the very general contravariance property of additive higher Chow groups. Using the moving lemma, we establish the structure of…

In this paper we study the MOR cryptosystem using finite classical Chevalley groups over a finite field of odd characteristic. In the process we develop an algorithm for these Chevalley groups in the same spirit as the row-column operation…

We develop the theory of difference algebraic groups in the case where we have finitely many pairwise commuting difference operators. We show that the defining ideal of a difference algebraic group is finitely generated as a difference…

We prove, under some mild hypothesis, that an \'etale cover of curves defined over a number field has infinitely many specializations into an everywhere unramified extension of number fields. This constitutes an "absolute" version of the…

The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair…

We prove a theorem on how a conclusion on homological dimension of a family of coherent sheaves over a scheme can be done from homological dimension of the restriction of this family to the reduction of the base.

We prove the definability, and actually the finiteness of the commutator width, of many commutator subgroups in groups definable in o-minimal structures. It applies in particular to derived series and to lower central series of solvable…

For a finite group $G$ and complex character $\chi\in\mathrm{Irr}(G)$ that restricts irreducibly to a normal subgroup $N\vartriangleleft G,$ we prove a theorem about Clifford correspondences between the characters of subgroups of $G$ that…