Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T06:11:05.749Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  24 November 2006

Kiran S. Kedlaya
Kiran S. Kedlaya
Affiliation:
Department of Mathematics, Room 2-165, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USAkedlaya@mit.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

rigid cohomologyFourier transformWeil conjectures14F3014G10
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 6 , November 2006 , pp. 1426 - 1450
Copyright
Foundation Compositio Mathematica 2006