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Nous développons une nouvelle stratégie pour comprendre la nature des obstructions aux déformations d’une représentation galoisienne globale réductible, impaire de dimension 2. Ces obstructions s’interprètent en termes de groupe de Šafarevič. D’après [BöMé], elles sont reliées à des conjecture arithmétiques classiques (Conjecture de Vandiver, conjecture de Greenberg). Dans cet article, nous introduisons un autre groupe de Šafarevič associé au corps fixe par . Nous comparons les deux groupes...
We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group over a complete local Noetherian ring of positive residue characteristic.
We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.
A perfect polynomial over is a polynomial that equals the sum of all its divisors. If then we say that is odd. In this paper we show the non-existence of odd perfect polynomials with either three prime divisors or with at most nine prime divisors provided that all exponents are equal to
Although Sarnak's conjecture holds for compact group rotations (irrational rotations, odometers), it is not even known whether it holds for all Jewett-Krieger models of such rotations. In this paper we show that it does, as long as the model is at the same a topological extension, via the same map that establishes the isomorphism, of an equicontinuous model. In particular, we recover (after [AKL]) that regular Toeplitz systems satisfy Sarnak's conjecture, and, as another consequence, so do...
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