Cubic structures, equivariant Euler characteristics and lattices of modular forms


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.


Ted Chinburg

Department of Mathematics
University of Pennsylvania David Rittenhouse Lab
209 South 33rd Street
Philadelphia, PA 19104-6395
United States

Georgios Pappas

Department of Mathematics
Michigan State University
East Lansing, MI 48824
United States

Martin J. Taylor

Department of Mathematics
University of Manchester
M60 1QD
United Kingdom