Rankin–Eisenstein classes in Coleman families
By David Loeffler, Sarah Livia Zerbes. 2015
78 citations recorded by the source corpus.
We show that the Euler system associated with Rankin–Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in p-adic Coleman families. We prove an explicit reciprocity law for these families and use this to prove cases of the Bloch–Kato conjecture for Rankin–Selberg convolutions.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5fdfa378182f893ace5cbe19afd4cca3de44013a
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Citations in the corpus
- Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, methodology): “This is the p-adic L-function used in [37].”
- Euler systems for GSp(4) (2017, methodology): “o allow suciently small positive values of the \slope" v p(t(p)), where t(p) is the eigenvalue of T(p) on f[3 w 2 ]. (Slope <1 is easy; slope <1 + amay be accessible, using the methods of [LZ16].) However, we stick with v p(t(p)) = 0 in the present paper for simplicity. 10.5. Lemma{Eisens”
- Rankin-Eisenstein classes for modular forms (2015, methodology): “aper). Moreover, the use of higher-weight modular forms means that our explicit reciprocity law can be generalised to non-ordinary Coleman families, as we shall show in the third paper in this series [LZ16]. 1.4. Acknowledgements. The authors are very grateful to Massimo Bertolini, Henri Darmon, and”
- Rankin--Eisenstein classes and explicit reciprocity laws (2015, methodology): “Thus their strategy requires a delicate study of the special fibres of the modular curves X1(Np ) in characteristic p, which is not needed in our approach; and our method is also amenable to generalisations to non-ordinary Coleman families, as we shall show in a subsequent paper [29].”