We construct a space of overconvergent modular forms of characteristic p, a compact operator on this space and we show that the characteristic series of this operator is the reduction modulo p of Coleman's universal series. We prove that finite slope overconvergent modular forms in positive characteristic can be deformed to characteristic 0.
Le halo spectral / F. Andreatta, A. Iovita, V. Pilloni. - In: ANNALES SCIENTIFIQUES DE L'ECOLE NORMALE SUPERIEURE. - ISSN 0012-9593. - 51:3(2018), pp. 603-655.
Le halo spectral
F. Andreatta;
2018
Abstract
We construct a space of overconvergent modular forms of characteristic p, a compact operator on this space and we show that the characteristic series of this operator is the reduction modulo p of Coleman's universal series. We prove that finite slope overconvergent modular forms in positive characteristic can be deformed to characteristic 0.
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