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Comptes Rendus Mathématique
Volume 341, n° 1
pages 21-24 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.007
Received : 7 Mars 2005 ;  accepted : 4 May 2005
Invariant de Serre et fibre de Milnor analytique
The Serre invariant and the analytic Milnor fiber
 

Johannes Nicaise a , Julien Sebag b
a KU Leuven, Departement de mathématiques, Celestijnenlaan 200B, 3001 Leuven, Belgique 
b Université Bordeaux I, institut mathématique de Bordeaux, laboratoire A2X, 351, cours de la Libération, 33405 Talence, France 

Résumé

Soit R un anneau de valuation discrète complet dʼégales caractéristiques. Nous étudions le comportement des invariants de Serre motiviques (dont nous raffinons la définition) après extension finie de R . Nous établissons une formule de trace, qui donne une interprétation cohomologique des invariants de Serre, en termes des nombres de Lefschetz de la monodromie sur les cycles proches. Pour citer cet article : J. Nicaise, J. Sebag, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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Abstract

In this Note, we refine the notion of motivic Serre invariants. We study the behaviour of these invariants under ramification. We establish a trace formula, which yields a cohomological interpretation of the motivic Serre invariants, in terms of the Lefschetz numbers of the monodromy action on the nearby cycles. To cite this article: J. Nicaise, J. Sebag, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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