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• W3211807101 abstract "We prove a fundamental conjecture of Rubin on the structure of local units in the anticyclotomic $mathbb{Z}_p$-extension of the unramified quadratic extension of $mathbb{Q}_p$ for $pgeq 5$ a prime. Rubin's conjecture underlies Iwasawa theory of the anticyclotomic deformation of a CM elliptic curve over the CM field at primes $p$ of good supersingular reduction, notably the Iwasawa main conjecture in terms of $p$-adic $L$-function. As a consequence, we prove an inequality in the $p$-adic Birch and Swinnerton-Dyer conjecture for Rubin's $p$-adic $L$-function. Rubin's conjecture is also an essential tool in our exploration of the arithmetic of Rubin's $p$-adic $L$-function, which includes a Bertolini--Darmon--Prasanna type formula." @default.
• W3211807101 created "2021-11-22" @default.
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• W3211807101 date "2021-11-01" @default.
• W3211807101 modified "2023-09-24" @default.
• W3211807101 title "Rubin's conjecture on local units in the anticyclotomic tower at inert primes" @default.
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• W3211807101 doi "https://doi.org/10.4007/annals.2021.194.3.8" @default.
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