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arXiv · 1012.1680

Iwasawa Theory for the Symmetric Square of a CM Modular Form at Inert Primes

Antonio Lei
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Abstract

Let f be a CM modular form and p an odd prime which is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by Delbourgo-Dabrowski, whereas the second one has a similar interpolating properties but corresponds to a different eigenvalue of the Frobenius. The symmetry between these two p-adic L-functions allows us to define the plus and minus p-adic L-functions à la Pollack. We also define the plus and minus p-Selmer groups analogous to Kobayashi's Selmer groups. We explain how to relate these two sets of objects via a main conjecture.

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Antonio Lei. 2011-08-16. Iwasawa Theory for the Symmetric Square of a CM Modular Form at Inert Primes. https://doi.org/10.1017/s0017089511000553

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