TY - JOUR

T1 - Rubin's conjecture on local units in the anticyclotomic tower at inert primes

AU - Burungale, Ashay A.

AU - Kobayashi, Shinichi

AU - Ota, Kazuto

N1 - Funding Information:
Keywords: CM elliptic curves, Iwasawa theory, local units, p-adic L-functions AMS Classification: Primary: 11G07, 11G15, 11R23. This work was partially supported by the NSF grant DMS 2001409, and the JSPS KAK-ENHI grants JP16K13742, JP17H02836, JP17K14173 and JP18J01237. © 2021 Department of Mathematics, Princeton University.
Publisher Copyright:
© 2021. Department of Mathematics, Princeton University

PY - 2021/11

Y1 - 2021/11

N2 - We prove a fundamental conjecture of Rubin on the structure of local units in the anticyclotomic Zp-extension of the unramified quadratic extension of Qp for p ≥ 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 super-singular reduction, notably the Iwasawa main conjecture in terms of the 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.

AB - We prove a fundamental conjecture of Rubin on the structure of local units in the anticyclotomic Zp-extension of the unramified quadratic extension of Qp for p ≥ 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 super-singular reduction, notably the Iwasawa main conjecture in terms of the 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.

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U2 - 10.4007/annals.2021.194.3.8

DO - 10.4007/annals.2021.194.3.8

M3 - Article

AN - SCOPUS:85129784874

SN - 0003-486X

VL - 194

SP - 943

EP - 966

JO - Annals of Mathematics

JF - Annals of Mathematics

IS - 3

ER -