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arXiv · 1607.05465

Periods of modular GL2-type abelian varieties and p-adic integration

Xavier Guitart·Marc Masdeu
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Abstract

Let F be a number field and N an integral ideal in its ring of integers. Let f be a modular newform over F of level Gamma0(N) with rational Fourier coefficients. Under certain additional conditions, Guitart-Masdeu-Sengun constructed a p-adic lattice which is conjectured to be the Tate lattice of an elliptic curve E whose L-function equals that of f. The aim of this note is to generalize this construction when the Hecke eigenvalues of f generate a number field of degree d >= 1, in which case the geometric object associated to f is expected to be, in general, an abelian variety A of dimension d. We also provide numerical evidence supporting the conjectural construction in the case of abelian surfaces.

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Xavier Guitart, Marc Masdeu. 2016-07-19. Periods of modular GL2-type abelian varieties and p-adic integration. https://arxiv.org/abs/1607.05465

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