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The Fields of Moduli for Polarized Abelian Varieties and for Curves

Published online by Cambridge University Press:  22 January 2016

Shoji Koizumi
Shoji Koizumi*
Affiliation:
Tokyo University of Education
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In the study of moduli of polarized abelian varieties and of curves as well as in the theory of complex multiplications, the notion of fields of moduli for structures plays an essential role. This notion was first introduced by Matsusaka [7] for polarized varieties with some pleasing properties and later was given a more comprehensible treatment by Shimura [10] in the case of polarized abelian varieties or polarized abelian varieties with some further structures. Both authors discussed fields of moduli not only in algebraic geometry of characteristic zero but also in that of positive characteristic, but in the latter case the definition of fields of moduli seems somewhat artificial and there have been no essential applications of them so far.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 48 , December 1972 , pp. 37 - 55
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1972

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