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 language | English (US) |
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Pages (from-to) | 361-378 |
Number of pages | 18 |
Journal | Annales Mathematiques du Quebec |
Volume | 48 |
Issue number | 2 |
DOIs | |
State | Published - Oct 2024 |
Keywords
- 11G10
- 11G25
- 14K20
- 14L05
- Abelian varieties
- Formal groups
- Ramification
ASJC Scopus subject areas
- General Mathematics