Wednesday 19 June 2013 h. 15:00, room 2BC60

Sophie Marques (Padova, Dip. Mat. and Bordeaux)

"An introduction to Ramification Theory for Number Fields"

Abstract

The question of prime decomposition in a finite extension of fields motivates classical ramification theory for field extensions. We propose to give a very little introduction to this deep subject which can also be extended to arithmetic geometry.

After recalling some basic facts around finite field extensions, we will explain how to do arithmetic in number fields. This will permit us to define the ramification for number field and to give some criteria permitting to decide which primes are ramified or not. Finally, we will study the particular case of quadratic extensions in order to see how we can apply this theory.

Rif. int. C. Marastoni, T. Vargiolu