scholarly journals Lifting the field of norms

10.5802/jep.2 ◽  
2014 ◽  
Vol 1 ◽  
pp. 29-38 ◽  
Author(s):  
Laurent Berger
Keyword(s):  
Field Of Norms

The field of norms functor and the Brückner-Vostokov formula

1997 ◽  
Vol 308 (1) ◽  
pp. 5-19 ◽  
Author(s):  
Viktor A. Abrashkin
Keyword(s):  
Field Of Norms

scholarly journals Facteurs epsilon p-adiques

2008 ◽  
Vol 144 (2) ◽  
pp. 439-483 ◽  
Author(s):  
Adriano Marmora
Keyword(s):  
Residue Field ◽  
Smooth Curve ◽  
Local System ◽  
Product Formula ◽  
Mixed Characteristic ◽  
Characteristic Case ◽  
Rank One ◽  
Epsilon Factors ◽  
Valuation Field ◽  
Field Of Norms

AbstractWe develop and study the epsilon factor of a ‘local system’ of p-adic coefficients over the spectrum of a complete discrete valuation field K with finite residue field of characteristic p>0. In the equal characteristic case, we define the epsilon factor of an overconvergent F-isocrystal over Spec(K), using the p-adic monodromy theorem. We conjecture a global formula, the p-adic product formula, analogous to Deligne’s formula for étale ℓ-adic sheaves proved by Laumon, which explains the importance of this local invariant. Namely, for an overconvergent F-isocrystal over an open subset of a projective smooth curve X, the constant of the functional equation of the L-series is expressed as a product of the local epsilon factors at the points of X. We prove the conjecture for rank-one overconvergent F-isocrystals and for finite unit-root overconvergent F-isocrystals. In the mixed characteristic case, we study the behavior of the epsilon factor by deformation to the field of norms.

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