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Cycles on Arithmetic Surfaces

Published online by Cambridge University Press:  04 December 2007

Ahmed Abbes
Ahmed Abbes
Affiliation:
CNRS UMR 7539, Institut Galileé, Université Paris-Nord, 93430 Villetaneuse, France. E-mail: abbes@math.univ-paris13.fr
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Abstract

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We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz fixed point formula for arithmetic surfaces, and give an application to a conjecture of Serre on the existence of Artin's representations for regular local rings of dimension 2 and unequal characteristic.

Keywords

arithmetic surfaceslocalized intersection theorybivariant classesLefschetz fixed point formulaArtin's representations
Type
Research Article
Information
Compositio Mathematica , Volume 122 , Issue 1 , May 2000 , pp. 23 - 111
Copyright
© 2000 Kluwer Academic Publishers