Sheffield Number Theory Group Reading Seminar
# Galois Representations
## Spring 2015 This term we will study Galois representations following mainly the lecture notes of Frazer Jarvis's graduate course.
The meetings will take place in room F-35 Hicks Building on Thursdays at 2pm.
## Talks:**Title:** Galois Theory and representations of profinite groups
**Speaker:** Dan
**Contents:** Brief review of infinite Galois theory and basic results related to representations of profinite groups. Main source is Section 1 and 2 of [J].
**Title:** Structure of G_Qp
**Speaker:** Haluk
**Contents:** A discussion of extensions of Qp and their Galois groups, inlcuding the Weil group. Main source is Section 3 of [J].
**Title:**Representations of G_Qp
**Speakers:** Jayanta + Tobias
**Contents:** Deligne-Groethendieck theorem, discussion of 1-dimensional representations and class field theory. The classification of 2-dimensional l-adic Galois representations and their reductions. Sections 5 and 6 of [J] should be summarized. Should be spread to two talks.
**Title:** Elliptic curves and associated Galois representations
**Speaker:** David
**Contents:** Goal is to discuss the mod l and l-adic representations coming from elliptic curves.
**Title:** Classical modular forms: Basics
**Speaker:** Rudolph
**Contents:** Basics, including newforms theory.
**Title:** Classical modular forms: Associated Galois representations
**Speaker:** Frazer
**Contents:** Discussion of results of Shimura and Deligne.
**Title:** Basics of automorphic representations
**Speaker:** Donggeon
**Contents:** Basic definitions, together with a discussion of the passage between classical newforms and cuspidal automorphic representations. May be spread to two talks, or skipped altogether depending on the audience's interests.
**Title:** Fontaine-Mazur Conjecture and Serre's Conjecture
**Speaker:**
**Contents:** Discussion of the statements
**Title:**An introduction to deformation theory of Galois representations
**Speaker:**
**Contents:** Discussion of basics up to the representability of the deformation functor. Lectures 1 and 2 of [G] should be summarized. May be spread to two talks.
## Materials:[B1] G.Boeckle. Lecture notes on Galois representations. Link [B2] G.Boeckle. Lecture notes on deformation theory of Galois representations (more advanced than those of Gouvea's below). Link [DS] F.Diamond, J.Shurman: Chapter 9 of their book has an elementary account of Galois representations. [DDT] H.Darmon, F.Diamond and R.Taylor. Long expository article on the proof of Fermat's Last Theorem. Link [F0] J.-M. Fontaine, Y. Ouyang. Book on Fontaine's theory of p-adic representations of G_Qp. Link [G] F.Gouvea: Expository article on deformation theory in the proceedings "Arithmetic Algebraic Geometry". [J] F.Jarvis. Notes from his 2006 course on Galois representations. Link [M] B. Mazur: Expository article discussing Galois representations among others. Link [R] K.Ribet. Expository article on Galois representations and modular forms. Link [T] R.Taylor. Extended version of his ICM talk on Galois representations. Link [W] G.Wiese: Lecture notes on Galois representations. Link |