p∞p^ ‐Selmer ranks of CM abelian varieties

Key Points

Key points are not available for this paper at this time.

Abstract

Abstract For an elliptic curve with complex multiplication over a number field, the ‐Selmer rank is even for all . Česnavičius proved this using the fact that admits a ‐isogeny whenever splits in the complex multiplication field, and invoking known cases of the ‐parity conjecture. We give a direct proof, and generalise the result to abelian varieties.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Jamie Bell (Thu,) studied this question.

synapsesocial.com/papers/68e65e37b6db6435875ecd1c https://doi.org/https://doi.org/10.1112/blms.13094

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1The 2-parity conjecture for elliptic curves with isomorphic 2-torsion2022 · 5 citations
2On the arithmetic of abelian varieties1972 · 181 citations
3A conjecture concerning rational points on cubic curves1954 · 23 citations
4The <i>p</i>-parity conjecture for elliptic curves with a <i>p</i>-isogeny2014 · 11 citations
5Root numbers and parity of ranks of elliptic curves2011 · 40 citations

Bookmark

View Full Paper