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Obstructions aux déformations de représentations galoisiennes réductibles et groupes de classes

Ariane Mézard (2005)

Journal de Théorie des Nombres de Bordeaux

Nous développons une nouvelle stratégie pour comprendre la nature des obstructions aux déformations d’une représentation galoisienne globale ρ ¯ 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 L fixe par ker ρ ¯ . Nous comparons les deux groupes...

Obstructions for deformations of complexes

Frauke M. Bleher, Ted Chinburg (2013)

Annales de l’institut Fourier

We develop two approaches to obstruction theory for deformations of derived isomorphism classes of complexes of modules for a profinite group G over a complete local Noetherian ring A of positive residue characteristic.

Odd perfect numbers of a special form

Tomohiro Yamada (2005)

Colloquium Mathematicae

We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.

Odd perfect polynomials over 𝔽 2

Luis H. Gallardo, Olivier Rahavandrainy (2007)

Journal de Théorie des Nombres de Bordeaux

A perfect polynomial over 𝔽 2 is a polynomial A ∈ 𝔽 2 [ x ] that equals the sum of all its divisors. If gcd ( A , x 2 + x ) = 1 then we say that A 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 2 .

Odometers and Toeplitz systems revisited in the context of Sarnak's conjecture

Tomasz Downarowicz, Stanisław Kasjan (2015)

Studia Mathematica

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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