Compositio Mathematica

Fourier transforms and $p$-adic ‘Weil II’

Kiran S. Kedlaya a1
a1 Department of Mathematics, Room 2-165, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Article author query
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We give a purity theorem in the manner of Deligne's ‘Weil II’ theorem for rigid cohomology with coefficients in an overconvergent $F$-isocrystal; the proof mostly follows Laumon's Fourier-theoretic approach, transposed into the setting of arithmetic $\mathcal{D}$-modules. This yields in particular a complete, purely $p$-adic proof of the Weil conjectures when combined with recent results on $p$-adic differential equations by André, Christol, Crew, Kedlaya, Matsuda, Mebkhout and Tsuzuki.

(Published Online November 24 2006)
(Received April 6 2004)
(Accepted May 10 2006)

Key Words: rigid cohomology; Fourier transform; Weil conjectures.

Maths Classification

14F30; 14G10.