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On étale covers of curves

Published online by Cambridge University Press:  01 July 1999

S. KAMIENNY  and
J. L. WETHERELL
S. KAMIENNY
Affiliation:
University of Southern California, Los Angeles, California; e-mail: [email protected], e-mail: [email protected]
J. L. WETHERELL
Affiliation:
University of Southern California, Los Angeles, California; e-mail: [email protected], e-mail: [email protected]
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Abstract

Let K be a number field with ring of integers R. For each integer g>1 we consider the collection of abelian, étale R-coverings f[ratio ]Y→X, where X and Y are connected proper curves over R and the genus of X is g. We ask the following question: is there a positive integer B = B(K, g) which bounds the degree of such coverings? In this note we provide partial results towards such a bound and study the relationship with bounds on torsion in abelian varieties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 127 , Issue 1 , July 1999 , pp. 1 - 5
Copyright
The Cambridge Philosophical Society 1999

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