Dwork Crystals III: From Excellent Frobenius Lifts Towards Supercongruences

Frits Beukers; Masha Vlasenko

doi:10.1093/imrn/rnad101

Dwork Crystals III: From Excellent Frobenius Lifts Towards Supercongruences

Frits Beukers^*, Masha Vlasenko

^*Corresponding author for this work

Institute of Mathematics of the Polish Academy of Sciences

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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.

Original language	English
Pages (from-to)	20433-20483
Number of pages	51
Journal	International Mathematics Research Notices
Volume	2023
Issue number	23
DOIs	https://doi.org/10.1093/imrn/rnad101
Publication status	Published - 1 Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 The Author(s). Published by Oxford University Press. All rights reserved.

Funding

This work was supported by the Netherlands Organisation for Scientific Research (NWO) [TOP1EW.15.313to F.B.]; and the National Science Centre of Poland (NCN) [UMO-2020/39/B/ST1/00940to M.V.]. Acknowledgments

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	TOP1EW.15.313
Narodowe Centrum Nauki	UMO-2020/39/B/ST1/00940to

Access to Document

10.1093/imrn/rnad101

rnad101Final published version, 600 KBLicence: CC BY

Cite this

@article{727cfcbed825410c8f5e66248a81d252,

title = "Dwork Crystals III: From Excellent Frobenius Lifts Towards Supercongruences",

abstract = "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.",

author = "Frits Beukers and Masha Vlasenko",

year = "2023",

month = dec,

day = "1",

doi = "10.1093/imrn/rnad101",

language = "English",

volume = "2023",

pages = "20433--20483",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "23",

}

TY - JOUR

T1 - Dwork Crystals III

T2 - From Excellent Frobenius Lifts Towards Supercongruences

AU - Beukers, Frits

AU - Vlasenko, Masha

PY - 2023/12/1

Y1 - 2023/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85179794217&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnad101

DO - 10.1093/imrn/rnad101

M3 - Article

AN - SCOPUS:85179794217

SN - 1073-7928

VL - 2023

SP - 20433

EP - 20483

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 23

ER -

Dwork Crystals III: From Excellent Frobenius Lifts Towards Supercongruences

Abstract

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this