Vol. 9, No. 1, 2015

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 8, 1765–1981
Issue 7, 1509–1763
Issue 6, 1243–1507
Issue 5, 995–1242
Issue 4, 749–993
Issue 3, 531–747
Issue 2, 251–530
Issue 1, 1–249

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editors' Interests
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Categories of abelian varieties over finite fields, I: Abelian varieties over $\mathbb{F}_{p}$

Tommaso Giorgio Centeleghe and Jakob Stix

Vol. 9 (2015), No. 1, 225–265
Abstract

We assign functorially a -lattice with semisimple Frobenius action to each abelian variety over Fp. This establishes an equivalence of categories that describes abelian varieties over Fp avoiding p as an eigenvalue of the Frobenius in terms of simple commutative algebra. This result extends the isomorphism classification of Waterhouse and Deligne’s equivalence for ordinary abelian varieties.

Keywords
abelian varieties, finite fields, Gorenstein rings, reflexive modules
Mathematical Subject Classification 2010
Primary: 11-02
Milestones
Received: 21 July 2014
Revised: 5 December 2014
Accepted: 6 January 2015
Published: 18 February 2015
Authors
Tommaso Giorgio Centeleghe
IWR
Universität Heidelberg
Im Neuenheimer Feld 368
D-69120 Heidelberg
Germany
Jakob Stix
Institut fĂĽr Mathematik
Goethe-Universität Frankfurt
Robert-Mayer-Straße 6–8
D-60325 Frankfurt am Main
Germany