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Modified proof of a local analogue of the Grothendieck conjecture

Victor Abrashkin (2010)

Journal de Théorie des Nombres de Bordeaux

A local analogue of the Grothendieck Conjecture is an equivalence between the category of complete discrete valuation fields K with finite residue fields of characteristic p ≠ 0 and the category of absolute Galois groups of fields K together with their ramification filtrations. The case of characteristic 0 fields K was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case p > 2 (but with no restrictions on the characteristic of K ). In this paper...

Modules différentiels sur les couronnes

Gilles Christol, Bernard Dwork (1994)

Annales de l'institut Fourier

Dans cet article, nous étudions les modules libres de type fini sur l’anneau ℋ [ d / d x ] où ℋ est l’anneau des éléments analytiques dans une couronne r 1 < | x | < r 2 de ℂ p . D’une part, nous définissons, pour chaque nombre r de [ r 1 , r 2 ] , un rayon de convergence “générique" et nous montrons que celui-ci dépend continûment de r . D’autre part, nous étudions l’existence et l’unicité d’un “antécédent de Frobenius".

Morales-Ramis Theorems via Malgrange pseudogroup

Guy Casale (2009)

Annales de l’institut Fourier

In this article we give an obstruction to integrability by quadratures of an ordinary differential equation on the differential Galois group of variational equations of any order along a particular solution. In Hamiltonian situation the condition on the Galois group gives Morales-Ramis-Simó theorem. The main tools used are Malgrange pseudogroup of a vector field and Artin approximation theorem.

Mosco convergence of sequences of homogeneous polynomials.

J. Ferrera (1998)

Revista Matemática Complutense

In this paper we give a characterization of uniform convergence on weakly compact sets, for sequences of homogeneous polynomials in terms of the Mosco convergence of their level sets. The result is partially extended for holomorphic functions. Finally we study the relationship with other convergences.

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension ≤ 4 and ≥ 11 . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real quadrics....

Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.

Laureano González-Vega, Guadalupe Trujillo (1997)

Revista Matemática de la Universidad Complutense de Madrid

The main purpose of this note is to show how Sturm-Habicht Sequence can be generalized to the multivariate case and used to compute the number of real solutions of a polynomial system of equations with a finite number of complex solutions. Using the same techniques, some formulae counting the number of real solutions of such polynomial systems of equations inside n-dimensional rectangles or triangles in the plane are presented.

Natural operators lifting vector fields to bundles of Weil contact elements

Miroslav Kureš, Włodzimierz M. Mikulski (2004)

Czechoslovak Mathematical Journal

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m -manifolds to the bundle functor K A of Weil contact elements and the subalgebra of fixed elements S A of the Weil algebra A is determined and the bijection between all natural affinors on K A and S A is deduced. Furthermore, the rigidity of the functor K A is proved. Requisite results about the structure of S A are obtained by a purely algebraic approach, namely the existence of nontrivial S A is discussed.

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