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Mirror symmetry and quantization of abelian varieties

Yu. I. Manin
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Abstract

The paper consists of two sections. The first section provides a new definition of mirror symmetry of abelian varieties making sense also over $p$-adic fields. The second section introduces and studies quantized theta-functions with two-sided multipliers, which are functions on non-commutative tori. This is an extension of an earlier work by the author. In the Introduction and in the Appendix the constructions of this paper are put into a wider context.

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Yu. I. Manin. 2000-05-15. Mirror symmetry and quantization of abelian varieties. https://arxiv.org/abs/math/0005143

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