259 research outputs found
Repr\'esentations galoisiennes p-adiques et (phi,tau)-modules
Let p be an odd prime number and K be a p-adic field. In this paper, we
develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the
p-cyclotomic extension by the extension K_infty obtained by adding to K a
compatible system of p^n-th roots of a fixed uniformizer pi of K. As a result,
we obtain a new classification of p-adic representations of G_K = Gal(Kbar/K)
by some (phi, \tau)-modules. We then make a link between the theory of
(phi,tau)-modules discussed above and the so-called theory of
(phi,N_nabla)$-modules developped by Kisin. As a corollary, we answer a
question of Tong Liu: we prove that, if K is a finite extension of Q_p, every
representation of G_K of E(u)-finite height is potentially semi-stable.Comment: 51 pages serious problem in Section 3 fixed; 2010-6
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