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Geometric Euler systems for locally isotropic motives

Published online by Cambridge University Press:  04 December 2007

Tom Weston
Tom Weston
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USAweston@math.berkeley.edu Department of Mathematics, University of California, Berkeley, CA 94720, USA
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Abstract

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In this paper, we construct a theory of geometric Euler systems, complementary to the arithmetic theory of Rubin, Kato and Perrin-Riou. We show that geometric Euler systems can be used to prove the finiteness of certain Galois representations of weight zero and we discuss a conjectural framework for the existence of geometric Euler systems for motivic Galois representations. We give applications to adjoint Selmer groups of certain classical and Drinfeld modular forms.

Keywords

Euler systemsSelmer groupsGalois representationsmodular forms11F80 (primary)11G1819E1519F27 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 2 , March 2004 , pp. 317 - 332
Copyright
Foundation Compositio Mathematica 2004