  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.

Algebraic Geometry;Number Theory