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

Ahmed Abbes·Takeshi Saito
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Abstract

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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Ahmed Abbes, Takeshi Saito. 2006-04-06. The characteristic class and ramification of an l-adic etale sheaf. https://doi.org/10.1007/s00222-007-0040-7

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