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Differential Modular Forms on Shimura Curves, I

Published online by Cambridge University Press:  04 December 2007

Alexandru Buium
Alexandru Buium
Affiliation:
University of New Mexico, Albuquerque, NM 87131, U.S.A. e-mail: buium@math.unm.edu
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Abstract

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The quotient of a Shimura curve by the isogeny equivalence relation is not an object of algebraic geometry. The paper shows how this quotient space becomes a geometric object in a more general geometry obtained from ‘usual algebraic geometry’, by adjoining a new operation; this operation looks like a ‘Fermat quotient’ and should be viewed as an arithmetic analogue of usual derivations.

Keywords

isogenymodular formsShimura curves
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 2 , November 2003 , pp. 197 - 237
Copyright
© 2003 Kluwer Academic Publishers