Current research in Number Theory is mostly concerned with studying representations of Galois groups. This modern point of view was pioneered by Artin in his pursuit of non-abelian generalizations of Class Field Theory and in the creation of his Artin L-function. Artin's work forms the foundation for the Langlands Program and Motivic L-functions, and will be the main focus of this seminar.

We will begin by covering the essentials of Representation Theory, which will then be used to reinterpret and generalize classical results in Number Theory, particularly with respect to L-functions. We will then take a detour into Ramification Theory in order to understand the origin of certain arithmetic factors appearing in the completed Artin L-function, whose construction and properties are the main goal of the seminar.

Depending on the interest of the students, we may also see how one can use the ideas above to construct Galois representations and L-functions from other arithmetic objects, such as elliptic curves or modular forms.

• Organisational meeting/distribution of topics: At M102 on Wednesday 05/02 at 14:30h.
• If you didn't/can't come to the organisational meeting, please send an email
  to "Julio.de-Mello-Bezerra@mathematik.uni-regensburg.de"
• Registration for course work/examination/ECTS: FlexNow

• Presentation: Giving a seminar talk of roughly 90 minutes

• Detailed written report of the seminar talk