On Arithmetic Invariants of Special Families of K3-Type Surfaces

Author: Can, Tran Thanh Trung

Year: 2024

Degree: Dissertation (Ph.D.)

Advisor: Mantovan, Elena

Committee Members: Graber, Thomas B.; Flach, Matthias; Zhao, Roy; Mantovan, Elena

Option: Mathematics

DOI: 10.7907/z5mc-g704

Abstract

This thesis studies applications of Shimura varieties in positive characteristic to questions on arithmetic invariants of special families of K3-type surfaces.

The first main result determines the Newton polygons and Artin invariants of 144 special families of K3-type surfaces. The second is a refinement of a conjecture of Serre for K3 surfaces over number field.

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• Trung-PhDthesis.pdf (application/pdf)