On the anticyclotomic Iwasawa theory of CM forms at supersingular primes
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Kâzim Büyükboduk [1]
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[1] Koç University
Koç University
Turquía
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 1, 2015, págs. 109-126
- Idioma: inglés
- DOI: 10.4171/RMI/828
- Texto completo no disponible (Saber más ...)
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Resumen
In this paper, we study the anticyclotomic Iwasawa theory of a CM form f of even weight w≥2 at a supersingular prime, generalizing the results in weight 2, due to Agboola and Howard. In due course, we are naturally lead to a conjecture on universal norms that generalizes a theorem of Perrin-Riou and Berger and another that generalizes a conjecture of Rubin (the latter seems linked to the local divisibility of Heegner points). Assuming the truth of these conjectures, we establish a formula for the variation of the sizes of the Selmer groups attached to the central critical twist of f as one climbs up the anticyclotomic tower. We also prove a statement which may be regarded as a form of the anticyclotomic main conjecture (without p-adic L-functions) for the central critical twist of f.
