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- W4294808051 abstract "Our goal in this article is to prove a form of $p$-adic Birch and Swinnerton-Dyer formula for the second derivative of the $p$-adic $L$-function associated to a newform $f$ which is non-crystalline semistable at $p$ at its central critical point, by expressing this quantity in terms of a $p$-adic (cyclotomic) regulator defined on an extended trianguline Selmer group. We also prove a two-variable version of this result for height pairings we construct by considering infinitesimal deformations afforded by a Coleman family passing through $f$. This, among other things, leads us to a proof of an appropriate version of Perrin-Riou's conjecture in this set-up." @default.
- W4294808051 created "2022-09-06" @default.
- W4294808051 creator A5020023156 @default.
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- W4294808051 date "2015-10-07" @default.
- W4294808051 modified "2023-09-25" @default.
- W4294808051 title "On the exceptional zeros of $p$-non-ordinary $p$-adic $L$-functions and a conjecture of Perrin-Riou" @default.
- W4294808051 doi "https://doi.org/10.48550/arxiv.1510.01915" @default.
- W4294808051 hasPublicationYear "2015" @default.
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