A note on local formulae for the parity of Selmer ranks

2024/09/12 by Morgan, Adam
#11G40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2409.08034

Abstract

In this note, we provide evidence for a certain twisted version of the parity conjecture for Jacobians, introduced in prior work of V. Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p-infinity Selmer groups.

Related

• Parity of ranks of Jacobians of curves
• 2^∞-Selmer Rank Parities via the Prym Construction
• The ℓ-parity conjecture over the constant quadratic extension
• p-Selmer ranks of CM abelian varieties
• Invariance of the parity conjecture for p-Selmer groups of elliptic curves in a D_2pⁿ-extension