On the root numbers of abelian varieties with real multiplication
Volume 203 / 2022
Acta Arithmetica 203 (2022), 137-163
MSC: Primary 11G10, 14K15; Secondary 11F80, 11G40.
DOI: 10.4064/aa210328-2-8
Published online: 11 April 2022
Abstract
Let $A/K$ be an abelian variety with real multiplication defined over a $p$-adic field $K$ with $p \gt 2$. We show that $A/K$ must have either potentially good or potentially totally toric reduction. In the former case we give formulas of the local root number of $A/K$ under the condition that inertia acts via an abelian quotient on the associated Tate module; in the latter we produce formulas without additional hypotheses.
