Categories of abelian varieties over finite fields II: Abelian varieties over Fq and Morita equivalence

  • The category of abelian varieties over Fq is shown to be anti-equivalent to a category of Z-lattices that are modules for a non-commutative pro-ring of endomorphisms of a suitably chosen direct system of abelian varieties over Fq. On full subcategories cut out by a finite set w of conjugacy classes of Weil q-numbers, the anti-equivalence is represented by what we call w-locally projective abelian varieties.

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Metadaten
Author:Tommaso Giorgio CentelegheGND, Jakob StixGND
URN:urn:nbn:de:hebis:30:3-842727
DOI:https://doi.org/10.1007/s11856-023-2536-2
ISSN:1565-8511
ArXiv Id:http://arxiv.org/abs/2112.14306
Parent Title (English):Israel Journal of Mathematics
Publisher:Springer
Place of publication:Berlin ; Heidelberg
Document Type:Article
Language:English
Date of Publication (online):2023/12/22
Date of first Publication:2023/12/22
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2024/07/16
Volume:257
Issue:1
Page Number:68
First Page:103
Last Page:170
HeBIS-PPN:520871669
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - CC BY - Namensnennung 4.0 International