Dwork crystals III: from excellent Frobenius lifts towards supercongruences

Autor:	Beukers, Frits, Vlasenko, Masha
Rok vydání:	2021
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry
Zdroj:	International Mathematics Research Notices, 2023
Druh dokumentu:	Working Paper
DOI:	10.1093/imrn/rnad101
Popis:	This paper is a continuation of our Dwork crystals series. Here we exploit the Cartier operation to prove supercongruences for expansion coefficients of rational functions. In the process it appears that excellent Frobenius lifts are a driving force behind supercongruences. Originally introduced by Dwork, these excellent lifts have occurred rather infrequently in the literature, and only in the context of families of elliptic curves and abelian varieties. In the final sections of this paper we present a list of examples that occur in the case of families of Calabi-Yau varieties. Comment: This is a minor revision of the previous version of the paper
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2105.14841 Zobrazit plný text záznamu View this record from Arxiv