Ramification of p-power torsion points of formal groups

Adrian Iovita, Jackson S. Morrow, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Let p be a rational prime, let F denote a finite, unramified extension of Qp, let K be the completion of the maximal unramified extension of Qp, and let K¯ be some fixed algebraic closure of K. Let A be an abelian variety defined over F, with good reduction, let A denote the Néron model of A over Spec(OF), and let A^ be the formal completion of A along the identity of its special fiber, i.e. the formal group of A. In this work, we prove two results concerning the ramification of p-power torsion points on A^. One of our main results describes conditions on A^, base changed to Spf(OK), for which the field K(A^[p])/K i s a tamely ramified extension where A^[p] denotes the group of p-torsion points of A^ over OK¯. This result generalizes previous work when A is 1-dimensional and work of Arias-de-Reyna when A is the Jacobian of certain genus 2 hyperelliptic curves.

Original languageEnglish (US)
Pages (from-to)361-378
Number of pages18
JournalAnnales Mathematiques du Quebec
Volume48
Issue number2
DOIs
StatePublished - Oct 2024

Keywords

  • 11G10
  • 11G25
  • 14K20
  • 14L05
  • Abelian varieties
  • Formal groups
  • Ramification

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Ramification of p-power torsion points of formal groups'. Together they form a unique fingerprint.

Cite this