Albanese and Fourier Transform: Positive Characteristic

This lecture delves into the concepts of Albanese varieties, canonical divisors, and Fourier-Mukai transforms in the context of algebraically closed fields. The instructor explains the relationship between the Albanese map and abelian varieties, the concept of GV-shifts, and the application of the Fourier transform in positive characteristic. The lecture also covers the Manin-Mumford conjecture, the Frobenius operator, and the Cartier operator on algebraic forms. The instructor demonstrates how these tools can be used to prove results related to the surjectivity of the Albanese map and the connected fibers in positive characteristic.