We construct p-adic iteration of the Gauss-Manin connection on overconvergent sheaves of de Rham classes on Hilbert modular varieties in the case p is unramified in the totally real field. This is a generalization of the work of Andreatta-Iovita in the case of elliptic curves, using a technique that marks an improvement on their approach in terms of convergence of the iterates of the connection.
OVERCONVERGENT MODULAR AND DE RHAM SHEAVES AND P-ADIC ITERATION OF THE GAUSS-MANIN CONNECTION / A. Kazi ; tutor: F. Andreatta ; coordinatore: D. Bambusi. Dipartimento di Matematica Federigo Enriques, 2022 Dec 21. 35. ciclo, Anno Accademico 2022.
OVERCONVERGENT MODULAR AND DE RHAM SHEAVES AND P-ADIC ITERATION OF THE GAUSS-MANIN CONNECTION
A. Kazi
2022
Abstract
We construct p-adic iteration of the Gauss-Manin connection on overconvergent sheaves of de Rham classes on Hilbert modular varieties in the case p is unramified in the totally real field. This is a generalization of the work of Andreatta-Iovita in the case of elliptic curves, using a technique that marks an improvement on their approach in terms of convergence of the iterates of the connection.
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