Geodesic
IWASAWA THEORY FOR THE SYMMETRIC SQUARE OF A CM MODULAR FORM AT INERT PRIMES
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 241-259

Voir la notice de l'article provenant de la source Cambridge University Press

Let f be a modular form with complex multiplication (CM) and p an odd prime that 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 and Dabrowski (A. Dabrowski and D. Delbourgo, S-adic L-functions attached to the symmetric square of a newform, Proc. Lond. Math. Soc. 74(3) (1997), 559–611), whereas the other 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 (R. Pollack, on the p-adic L-function of a modular form at a supersingular prime, Duke Math. J. 118(3) (2003), 523–558). We also define the plus and minus p-Selmer groups analogous to the ones defined by Kobayashi (S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152(1) (2003), 1–36). We explain how to relate these two sets of objects via a main conjecture.
DOI : 10.1017/S0017089511000553
Mots-clés : 11R23, 11F80 
LEI, ANTONIO. IWASAWA THEORY FOR THE SYMMETRIC SQUARE OF A CM MODULAR FORM AT INERT PRIMES. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 241-259. doi: 10.1017/S0017089511000553
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