https://scholars.lib.ntu.edu.tw/handle/123456789/624829
Title: | On the nonvanishing of generalised Kato classes for elliptic curves of rank 2 | Authors: | Castella F Hsieh M.-L. MING-LUN HSIEH |
Issue Date: | 2022 | Journal Volume: | 10 | Source: | Forum of Mathematics, Sigma | Abstract: | Let E/Q be an elliptic curve and p > 3 be a good ordinary prime for E and assume that L(E, 1)=0 with root number+1 (so ords=1 L(E, s) ≥ 2)). A construction of Darmon-Rotger attaches to E and an auxiliary weight 1 cuspidal eigenform g such that L(E, ad(g), 1) ≠ =0, a Selmer class κp ∈ Sel(Q,VpE), and they conjectured the equivalence {equation presented} In this article, we prove the first cases on Darmon-Rotger's conjecture when the auxiliary eigenform g has complex multiplication. In particular, this provides a new construction of nontrivial Selmer classes for elliptic curves of rank 2. © |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85125092194&doi=10.1017%2ffms.2021.85&partnerID=40&md5=5a6c97ac4beb687b91d765526b2c703c https://scholars.lib.ntu.edu.tw/handle/123456789/624829 |
ISSN: | 20505094 | DOI: | 10.1017/fms.2021.85 |
Appears in Collections: | 數學系 |
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