Alvaro Gonzalez Hernandez

Explicit theory of Kummer surfaces in characteristic two

Kummer surfaces are an essential tool for performing explicit computations with the Jacobians of genus two curves. While the theory behind these surfaces over fields of characteristic zero is well-known, there are still questions regarding the same theory over fields of characteristic two. In this talk, I will provide answers to some of these questions and explain how the characteristics zero and two interact when one considers a Kummer surface defined over a number field and studies its reduction modulo a prime lying above two. This will be showcased via explicit examples of Kummer surfaces and Jacobians associated with genus two curves.