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 -