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. ((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.
ANDREATTA, FABRIZIO
BAMBUSI, DARIO PAOLO
p-adic modular form; Hilbert modular form
Settore MAT/02 - Algebra
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. ((35. ciclo, Anno Accademico 2022.
Doctoral Thesis
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/949088
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