Analyse micro-locale l-adique en caracteristique p>0: Le cas d'un trait

Details Analyse micro-locale l-adique en caracteristique p>0: Le cas d'un trait Analyse micro-locale l-adique en caracteristique p>0: Le cas d'un trait

2006-02-14

arxiv.org/abs/math/0602285v3

Publication of the Research Institute for Mathematical Sciences 45-1 (2009) 25-74

Mathematics

Algebraic Geometry

36 pages, LaTeX; Modified contents mostly in Premiere partie, 36 pages, Latex; Minor change, adding a little more detail etc

Scientific paper

We develop, for an l-adic etale sheaf on a complete trait of characteristic p>0, the notion of characteristic variety. Our approach, inspired by the microlocal analysis of Kashiwara and Schapira, is a complement to our ramification theory for local fields with general residue fields. We formulate the main property that should be satisfied by the characteristic variety (the isogeny conjecture), and prove it for rank one sheaves unconditionally on the trait, or unconditionally on the sheaf if the residue field of the trait is perfect.

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