Power Towers: Foliations and Galois Theory in Positive Characteristic

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，Jia Jia 贾甲

Speaker：

Przemysław Grabowski

University of Amsterdam

Time：

Fri., 15:30-16:30, May. 9, 2025

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title

Power Towers: Foliations and Galois Theory in Positive Characteristic

The talk will discuss power towers. This is a new notion that I developed in my PhD thesis (2025). A power tower should be thought to be a foliation in positive characteristic. In particular, it is a simultaneous generalization of fibrations and purely inseparable morphisms. We will build a Galois theory for power towers. We will show how it connects to characteristic zero. Finally, we will apply the theory of power towers to obtain a formula for pullbacks of canonical divisors with respect to arbitrary purely inseparable morphism, then we derive some simple new theorems about unirationality modulo p from this formula.