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

• Autores: Ahmed Abbes, Takeshi Saito
• Localización: Inventiones mathematicae, ISSN 0020-9910, Vol. 168, Nº. 3, 2007, págs. 567-612
• Idioma: inglés
• DOI: 10.1007/s00222-007-0040-7
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• Resumen

  • We introduce the characteristic class of an l-adic étale sheaf using a cohomological pairing due to Verdier (SGA5). As a consequence of the Lefschetz¿Verdier trace formula, its trace computes the Euler¿Poincaré 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 [17] and the other is the 0-cycle class defined by Kato for rank 1 sheaves in [16].