On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes

Cited 6 time in webofscience Cited 0 time in scopus
  • Hit : 121
  • Download : 0
Let E/Q be an elliptic curve and p an odd prime where E has good reduction, and assume that E admits a rational p-isogeny. In this paper we study the anticyclotomic Iwasawa theory of E over an imaginary quadratic field in which p splits, which we relate to the anticyclotomic Iwasawa theory of characters by a variation of the method of Greenberg-Vatsal. As a result of our study we obtain proofs (under relatively mild hypotheses) of PerrinRiou's Heegner point main conjecture, a p-converse to the theorem of GrossZagier and Kolyvagin, and the p-part of the Birch-Swinnerton-Dyer formula in analytic rank 1, for Eisenstein primes p.
Publisher
SPRINGER HEIDELBERG
Issue Date
2022-02
Language
English
Article Type
Article
Citation

INVENTIONES MATHEMATICAE, v.227, no.2, pp.517 - 580

ISSN
0020-9910
DOI
10.1007/s00222-021-01072-y
URI
http://hdl.handle.net/10203/292116
Appears in Collection
RIMS Journal Papers
Files in This Item
There are no files associated with this item.
This item is cited by other documents in WoS
⊙ Detail Information in WoSⓡ Click to see webofscience_button
⊙ Cited 6 items in WoS Click to see citing articles in records_button

qr_code

  • mendeley

    citeulike


rss_1.0 rss_2.0 atom_1.0