Abstract

This talk aims to give a quick introduction to theory of p-adic integration. It consists of two parts: 

 

1. Coleman Integration.

In the first talk, we will give an introduction to the theory of Coleman p-adic integration. It allows us to uniquely integrate differential 1-forms on certain varieties defined over a p-adic field and has profound applications to arithmetic geometry due to its computability.

 

2. Finite polynomial cohomology.

After introducing Coleman integration, we proceed to talk about its generalization, finite polynomial cohomology à la Besser. This theory makes it possible to integrate higher differential forms. Moreover, it shows that p-adic Abel-Jacobi maps can be interpreted as p-adic integration, which is in accordance with the complex case. We also established a generalization of finite polynomial cohomology to more general coefficients rather than the structure sheaf. 

 

 

Organizer: Ming-Lun Hsieh (NTU)