The characteristic class and ramification of an l-adic etale sheaf

Details The characteristic class and ramification of an l-adic etale sheaf The characteristic class and ramification of an l-adic etale sheaf

2006-04-06

arxiv.org/abs/math/0604121v1

Inventiones Mathematicae 168 No. 3 (2007) 567-612

Mathematics

Algebraic Geometry

45 pages, Latex

Scientific paper

10.1007/s00222-007-0040-7

We introduce the characteristic class of an l-adic etale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz-Verdier trace formula, its trace computes the Euler-Poincare characteristic of the sheaf. We compare the characteristic class to two other invariants arising from ramification theory. One is the Swan class of Kato-Saito (math.AG/0402010) and the other is the 0-cycle class defined by Kato for rank 1 sheaves.

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