JournalsrmiVol. 31, No. 1pp. 109–126

On the anticyclotomic Iwasawa theory of CM forms at supersingular primes

  • Kâzim Büyükboduk

    Koç University, Istanbul, Turkey
On the anticyclotomic Iwasawa theory of CM forms at supersingular primes cover
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Abstract

In this paper, we study the anticyclotomic Iwasawa theory of a CM form ff of even weight w2w ≥ 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 ff 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 pp-adic LL-functions) for the central critical twist of ff.

Cite this article

Kâzim Büyükboduk, On the anticyclotomic Iwasawa theory of CM forms at supersingular primes. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 109–126

DOI 10.4171/RMI/828