This PhD thesis is divided into two parts, collecting two independent pieces of work I completed during my PhD, both in the realm of number theory and arithmetic geometry. The first part presents a joint work with J. Yelton, regarding semistable models of hyperelliptic curves in the wild case. To this subject, which was already the topic of my MSc. thesis, I devoted part of my research work during my PhD, until completing it during summer 2022. The second part of this thesis discusses some research findings related to a completely unrelated topic proposed to me by my PhD advisor Fabrizio Andreatta, namely the one of geometric constructions of differential operators on sheaves of p-adic modular forms.
SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS / L. Fiore ; tutor: F. Andreatta. Dipartimento di Matematica Federigo Enriques, 2023. 36. ciclo, Anno Accademico 2023/2024.
SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS
L. Fiore
2024
Abstract
This PhD thesis is divided into two parts, collecting two independent pieces of work I completed during my PhD, both in the realm of number theory and arithmetic geometry. The first part presents a joint work with J. Yelton, regarding semistable models of hyperelliptic curves in the wild case. To this subject, which was already the topic of my MSc. thesis, I devoted part of my research work during my PhD, until completing it during summer 2022. The second part of this thesis discusses some research findings related to a completely unrelated topic proposed to me by my PhD advisor Fabrizio Andreatta, namely the one of geometric constructions of differential operators on sheaves of p-adic modular forms.File | Dimensione | Formato | |
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