### The local reciprocity map: finding an explicit formula for a canonical isomorphism

**Newton , R ***(Cambridge)*

Thursday 15 April 2010, 14:00-14:20

Seminar Room 1, Newton Institute

#### Abstract

I will start by defining the p-adic numbers, the classic example of a local field. I will go on to state the existence of the local reciprocity map and describe the cases for which an explicit formula has been found. I will end by trying to explain what makes it difficult to compute local reciprocity in the remaining cases.