Cubic structures, equivariant Euler characteristics and lattices of modular form

Chinburg, Ted and Pappas, Georgios and Taylor, Martin J. (2007) Cubic structures, equivariant Euler characteristics and lattices of modular form. Annals of Mathematics. ISSN 0003-486x (Unpublished)

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Abstract

We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective at schemes over $\Z$ with a tame action of a finite abelian group. This formula supports a conjecture concerning the extent to which such equivariant Euler characteristics may be determined from the restriction of the sheaf to an infinitesimal neighborhood of the fixed point locus. Our results are applied to study the module structure of modular forms having Fourier coeficients in a ring of algebraic integers, as well as the action of diamond Hecke operators on the Mordell-Weil groups and Tate-Shafarevich groups of Jacobians of modular curves.

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 11 Number theory MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry
Depositing User:	Ms Lucy van Russelt
Date Deposited:	21 May 2007
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/802

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