SEMISTABLE MODELS OF HYPERELLIPTIC CURVES IN THE WILD CASE & DIFFERENTIAL OPERATORS ON P-ADIC MODULAR FORMS

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.

Grantor dc:publisher

Università degli Studi di Milano

Year dc:date

2024

Author dc:creator

• FIORE, LEONARDO

Contributors dc:contributor

• tutor: F. Andreatta
• L. Fiore
• ANDREATTA, FABRIZIO

• semistable model
• wild cover
• p-adic modular form
• theta operator
• Igusa varieties
• Settore MAT/02 - Algebra

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

http://dx.doi.org/10.13130/fiore-leonardo_phd2024-03-07
10.13130/fiore-leonardo_phd2024-03-07

OAI identifier oai:identifier

oai:air.unimi.it:2434/1027770