Matches in SemOpenAlex for { <https://semopenalex.org/work/W2795337013> ?p ?o ?g. }
- W2795337013 abstract "Let $B$ be a simple CM abelian variety over a CM field $E$, $p$ a rational prime. Suppose that $B$ has potentially ordinary reduction above $p$ and is self-dual with root number $-1$. Under some further conditions, we prove the generic non-vanishing of (cyclotomic) $p$-adic heights on $B$ along anticyclotomic $mathbb{Z}_{p}$-extensions of $E$. This provides evidence towards Schneider's conjecture on the non-vanishing of $p$-adic heights. For CM elliptic curves over $mathbb{Q}$, the result was previously known as a consequence of work of Bertrand, Gross--Zagier and Rohrlich in the 1980s. Our proof combines non-vanishing results for Katz $p$-adic $L$-functions and a Gross--Zagier formula relating the latter to families of rational points on $B$." @default.
- W2795337013 created "2018-04-06" @default.
- W2795337013 creator A5042417647 @default.
- W2795337013 creator A5087147472 @default.
- W2795337013 date "2018-03-25" @default.
- W2795337013 modified "2023-09-27" @default.
- W2795337013 title "On the non-vanishing of $p$-adic heights on CM abelian varieties, and the arithmetic of Katz $p$-adic $L$-functions" @default.
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