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IWASAWA THEORY FOR THE SYMMETRIC SQUARE OF A CM MODULAR FORM AT INERT PRIMES

Published online by Cambridge University Press:  12 December 2011

ANTONIO LEI
ANTONIO LEI*
Affiliation:
School of Mathematical Sciences, Monash University, Clayton, VIC 3800, Australia e-mail: antonio.lei@monash.edu
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Abstract

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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.

Keywords

11R2311F80
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 241 - 259
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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