Geodesic
Cubic structures, equivariant Euler characteristics and lattices of modular forms
Ted Chinburg1 ; Georgios Pappas2 ; Martin J. Taylor3
1 Department of Mathematics<br/>University of Pennsylvania David Rittenhouse Lab<br/>209 South 33rd Street<br/>Philadelphia, PA 19104-6395<br/>United States
2 Department of Mathematics<br/>Michigan State University<br/>East Lansing, MI 48824<br/>United States
3 Department of Mathematics<br/>University of Manchester<br/>M60 1QD<br/>United Kingdom
Annals of mathematics, Tome 170 (2009) no. 2, pp. 561-608.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 flat schemes over $\mathbb{Z}$ 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 coefficients 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.
DOI : 10.4007/annals.2009.170.561

Ted Chinburg 1 ; Georgios Pappas 2 ; Martin J. Taylor 3

1 Department of Mathematics<br/>University of Pennsylvania David Rittenhouse Lab<br/>209 South 33rd Street<br/>Philadelphia, PA 19104-6395<br/>United States
2 Department of Mathematics<br/>Michigan State University<br/>East Lansing, MI 48824<br/>United States
3 Department of Mathematics<br/>University of Manchester<br/>M60 1QD<br/>United Kingdom 
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Ted Chinburg; Georgios Pappas; Martin J. Taylor. Cubic structures, equivariant Euler characteristics and lattices of modular forms. Annals of mathematics, Tome 170 (2009) no. 2, pp. 561-608. doi : 10.4007/annals.2009.170.561. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.170.561/

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