Back to Algebraic Geometry Seminar: Fall 2026
Algebraic Geometry Seminar
Date: Tuesday, Sep 29, 2026
Time: 3:30PM - 4:30PM
Location: LCB 215
Fabio Bernasconi
Sapienza University of Rome
Title |
On smooth projective surfaces over Z |
Abstract |
A folklore question to arithmetic geometry (attributed to Shafarevich and Grothendieck) asks what are the smooth projective varieties of dimension (d) over (\operatorname{Spec}(\mathbb Z)). In relative dimensions (0) and (1), a complete answer is known, thanks to the work of Minkowski, Gauss, and Abrashkin–Fontaine, which I will briefly recall. Starting in relative dimension (2), the problem remains open. I will discuss some of the known restrictions and present a complete classification in the case of surfaces of Kodaira dimension at most 0, obtained in joint work with G. Martin and Zs. Patakfalvi. If time permits, I will also explain some examples and phenomena in higher dimensions. |
Algebraic Geometry