Displaying similar documents to “Frobenius modules and Galois representations”

Some new directions in p -adic Hodge theory

Kiran S. Kedlaya (2009)

Journal de Théorie des Nombres de Bordeaux

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We recall some basic constructions from p -adic Hodge theory, then describe some recent results in the subject. We chiefly discuss the notion of B -pairs, introduced recently by Berger, which provides a natural enlargement of the category of p -adic Galois representations. (This enlargement, in a different form, figures in recent work of Colmez, Bellaïche, and Chenevier on trianguline representations.) We also discuss results of Liu that indicate that the formalism of Galois cohomology,...

On Galois structure of the integers in cyclic extensions of local number fields

G. Griffith Elder (2002)

Journal de théorie des nombres de Bordeaux

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Let p be a rational prime, K be a finite extension of the field of p -adic numbers, and let L / K be a totally ramified cyclic extension of degree p n . Restrict the first ramification number of L / K to about half of its possible values, b 1 > 1 / 2 · p e 0 / ( p - 1 ) where e 0 denotes the absolute ramification index of K . Under this loose condition, we explicitly determine the ℤ p [ G ] -module structure of the ring of integers of L , where ℤ p denotes the p -adic integers and G denotes the Galois group Gal ( L / K ) . In the process of determining...

On a general difference Galois theory I

Shuji Morikawa (2009)

Annales de l’institut Fourier

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We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic 0 , we attach its Galois group, which is a group of coordinate transformation.