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

[摘要] 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.

[学科分类] 数学（综合）