Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ℚ, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.
Overconvergent modular sheaves and modular forms for GL 2/F / F. Andreatta, A. Iovita, G. Stevens. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 201:1(2014 Jan), pp. 299-359. [10.1007/s11856-014-1045-8]
Overconvergent modular sheaves and modular forms for GL 2/F
F. AndreattaPrimo
;
2014
Abstract
Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ℚ, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.File | Dimensione | Formato | |
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