11 research outputs found
Product formula for p-adic epsilon factors
Let X be a smooth proper curve over a finite field of characteristic p. We
prove a product formula for p-adic epsilon factors of arithmetic D-modules on
X. In particular we deduce the analogous formula for overconvergent
F-isocrystals, which was conjectured previously. The p-adic product formula is
the equivalent in rigid cohomology of the Deligne-Laumon formula for epsilon
factors in l-adic \'etale cohomology (for a prime l different from p). One of
the main tools in the proof of this p-adic formula is a theorem of regular
stationary phase for arithmetic D-modules that we prove by microlocal
techniques.Comment: Revised version: some proofs and constructions detailed, notation
improved, index of notation added ; 88 page
Locally analytic representations and sheaves on the Bruhat-Tits building
Let L be a finite field extension of Q_p and let G be the group of L-rational
points of a split connected reductive group over L. We view G as a locally
L-analytic group with Lie algebra g. We define a functor from admissible
locally analytic G-representations with prescribed infinitesimal character to a
category of equivariant sheaves on the Bruhat-Tits building of G. For smooth
representations, the corresponding sheaves are closely related to the sheaves
constructed by S. Schneider and U. Stuhler. The functor is also compatible, in
a certain sense, with the localization of g-modules on the flag variety by A.
Beilinson and J. Bernstein.Comment: Replaces earlier version. Exposition shortened and improved in
several places, and new material and examples added. In particular, section
11 is new.