Related papers: A general theory of Andr\'e's solution algebras
We study torsors for groups defined by algebraic difference equations. Our main result provides necessary and sufficient conditions on the base difference field for all such torsors to be trivial. We also present an application to the…
This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic…
We introduce the existence of a Genus-Type Theory that generalizes classical genus theory by linking fractional ideals of number fields to structures built from their Galois groups and associated Diophantine equations, as formally stated in…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
Differential equations have arithmetic analogues in which derivatives are replaced by Fermat quotients; these analogues are called arithmetic differential equations and the present paper is concerned with the "linear" ones. The equations…
For a field k$with an automorphism \sigma and a derivation \delta, we introduce the notion of liouvillian solutions of linear difference-differential systems {\sigma(Y) = AY, \delta(Y) = BY} over k and characterize the existence of…
One of the traditional applications of relation algebras is to provide a setting for infinite-domain constraint satisfaction problems. Complexity classification for these computational problems has been one of the major open research…
In an earlier paper, the authors introduced partial translation algebras as a generalisation of group C*-algebras. Here we establish an extension of partial translation algebras, which may be viewed as an excision theorem in this context.…
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
We extend some properties of pullbacks which are known to hold in a Mal'tsev context to the more general context of Gumm categories. The varieties of universal algebras which are Gumm categories are precisely the congruence modular ones.…
We propose in this paper a Galois theory of $q$-difference equations where q is a root of unity. This theory is the q difference analogue of the Galois theory of iterative differential equations, that is differential equations over fields…
We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and…
We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finite groups and a conjugation of the group algebra of the…
We present a maximal class of analytic functions, elements of which are in one-to-one correspondence with their asymptotic expansions. In recent decades it has been realized (B. Malgrange, J. Ecalle, J.-P. Ramis, Y. Sibuya et al.), that the…
Motivated by the study of algebraic classes in mixed characteristic we define a countable subalgebra of $\bar{\mathbb{Q}}_p$ which we call the algebra of Andr\'e's $p$-adic periods. We construct a tannakian framework to study these periods.…
Using model theory and differential algebra, we give necessary conditions for algebraic ordinary differential equations to have a complex Pfaffian solution on some complex domain. These tools also allow us to give many examples of algebraic…
Discussed here is descent theory in the differential context where everything is equipped with a differential operator. To answer a question personally posed by A. Pianzola, we determine all twisted forms of the differential Lie algebras…
This book deals with the theory of generalized algebraic transformations, which is elaborated with the aim to provide a relatively simple theoretical tool that enables an exact treatment of diverse more complex lattice-statistical models.…
The purpose of this work is twofold: to expose the existing similarities between the generalizations of the Tannaka and Galois theories, and on the other hand, to develop in detail our own treatment of part of the content of Joyal and…
In this paper we develop a theory of class invariants associated to $p$-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to…