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Calabi-Yau Manifolds Over Finite Fields, I

Abstract:

We study Calabi-Yau manifolds defined over finite fields. These manifolds have parameters, which now also take values in the field and we compute the number of rational points of the manifold as a function of the parameters. The intriguing result is that it is possible to give explicit expressions for the number of rational points in terms of the periods of the holomorphic three-form. We show also, for a one parameter family of quintic threefolds, that the number of rational points of the man...

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Role:
Author
Publication date:
2000-12-24
URN:
uuid:9ac032e9-1e8e-47d4-8a42-542859a6025e
Source identifiers:
1084
Local pid:
pubs:1084
Keywords:

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