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Isogeny Covariant Differential Modular Forms and the Space of Elliptic Curves up to Isogeny

Published online by Cambridge University Press:  04 December 2007

Mugurel A. Barcau
Mugurel A. Barcau
Affiliation:
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, U.S.A. e-mail: [email protected] and Institute of Mathematics of the Romanian Academy, PO Box 1-764, RO-70700 Bucharest, Romania
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Abstract

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The purpose of this article is to develop the theory of differential modular forms introduced by A. Buium. The main points are the construction of many isogeny covariant differential modular forms and some auxiliary (nonisogeny covariant) forms and an extension of the ‘classical theory’ of Serre differential operators on modular forms to a theory of ‘δ-Serre differential operators’ on differential modular forms. As an application, we shall give a geometric realization of the space of elliptic curves up to isogeny.

Keywords

differential modular formsisogenyisogeny covariance
Type
Research Article
Information
Compositio Mathematica , Volume 137 , Issue 3 , July 2003 , pp. 237 - 273
Copyright
© 2003 Kluwer Academic Publishers