Purely additive reduction of abelian varieties with torsion

Mentzelos Melistas*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)

Abstract

Let OK be a discrete valuation ring with fraction field K of characteristic 0 and algebraically closed residue field k of characteristic p > 0. Let A/K be an abelian variety of dimension g with a K-rational point of order p. In this article, we are interested in the reduction properties that A/K can have. After discussing the general case, we specialize to g = 1, and we study the possible Kodaira types that can occur.
Original languageEnglish
Pages (from-to)21-39
Number of pages19
JournalJournal of Number Theory
Volume239
Early online date24 Nov 2021
DOIs
Publication statusPublished - Oct 2022
Externally publishedYes

Keywords

  • Abelian variety
  • Purely additive reduction
  • Néron model
  • Torsion point
  • Kodaira type
  • n/a OA procedure

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