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2015 | OriginalPaper | Chapter

Introduction to Arithmetic Mirror Symmetry

Author: Andrija Peruničić

Published in: Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Publisher: Springer New York

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Abstract

We describe how to find period integrals and Picard-Fuchs differential equations for certain one-parameter families of Calabi-Yau manifolds. These families can be seen as varieties over a finite field, in which case we show in an explicit example that the number of points of a generic element can be given in terms of p-adic period integrals. We also discuss several approaches to finding zeta functions of mirror manifolds and their factorizations. These notes are based on lectures given at the Fields Institute during the thematic program on Calabi-Yau Varieties: Arithmetic, Geometry, and Physics.
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Metadata
Title
Introduction to Arithmetic Mirror Symmetry
Author
Andrija Peruničić
Copyright Year
2015
Publisher
Springer New York
DOI
https://doi.org/10.1007/978-1-4939-2830-9_15

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