https://scholars.lib.ntu.edu.tw/handle/123456789/624836
標題: | Heegner cycles and p-adic L-functions | 作者: | Castella F Hsieh M.-L. MING-LUN HSIEH |
公開日期: | 2018 | 卷: | 370 | 期: | 44563 | 起(迄)頁: | 567-628 | 來源出版物: | Mathematische Annalen | 摘要: | In this paper, we deduce the vanishing of Selmer groups for the Rankin–Selberg convolution of a cusp form with a theta series of higher weight from the nonvanishing of the associated L-value, thus establishing the rank 0 case of the Bloch–Kato conjecture in these cases. Our methods are based on the connection between Heegner cycles and p-adic L-functions, building upon recent work of Bertolini, Darmon and Prasanna, and on an extension of Kolyvagin’s method of Euler systems to the anticyclotomic setting. In the course of the proof, we also obtain a higher weight analogue of Mazur’s conjecture (as proven in weight 2 by Cornut–Vatsal), and as a consequence of our results, we deduce from Nekovs work a proof of the parity conjecture in this setting. © 2017, Springer-Verlag Berlin Heidelberg. |
URI: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85009881914&doi=10.1007%2fs00208-017-1517-3&partnerID=40&md5=6a379ea4bd759cba3c880124531402c7 https://scholars.lib.ntu.edu.tw/handle/123456789/624836 |
ISSN: | 00255831 | DOI: | 10.1007/s00208-017-1517-3 |
顯示於: | 數學系 |
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