Learning Seminar in Algebra, Number Theory, and Representation Theory

Fall 2024 

[3pm, Neckers 356]

[11-4-2024] 

Topic:  Proofs of LLC of GL(2) and SL(2)

Reference:  [BH06, §28], [Wed08, §3.1], [Tat79, §2 & §4],  [GK82]

[10-28-2024] 

Topic:  l-adic representations of p-adic fields and L-parameters of GL(2) II

Reference: [Wed08, §3.1], [Tat79, §2 & §4], [BH06, §32], [FO, §2.3]

[10-21-2024] 

Topic:  l-adic representations of p-adic fields and L-parameters of GL(2) I

Reference: [Wed08, §3.1], [Tat79, §2 & §4], [BH06, §32], [FO, §2.3]

[10-7-2024] 

Topic: SL(2) theories from GL(2)

Reference: [GK82, §2], [Tad92, §2], [HS12, §2] 

[9-30-2024] 

Topic: p-adic side of GL(2) theories

Reference: [Kud94, Sections 1 and 2],  [Wed08, §2]

[9-23-2024] 

Topic: Review on general SL(2) theories and Introduction to Algebraic Tori

Reference: My note (Example 5.58 + Sec 5.1), [Bor79, Section 8.5],  [Mur05, §4], [Spr98, §3.2].

Spring 2024 

[1pm, Neckers 278/356]

[4-18-2024] 

Topic:  Overview of l-adic Galois Representations II

Reference:  [FO, Section 1.1 and 1.3], [BH06, Section 35] ,  My note (Example 5.58 + Sec 5.1). 

[4-11-2024] 

Topic:  Overview of l-adic Galois Representations I

Reference:  [Bor79] ,  [FO, Section 1.1] 

[4-4-2024] 

Topic:  Introduction to Algebraic Groups and L-groups II

Reference:  [Bor91, Chapter I], [Spr98, Chapter 10]

[3-28-2024] 

Topic:  Introduction to Algebraic Groups and L-groups I

Reference: [Bor79], [Bor91], [Mur09], [Spr98] 

Bibliography

[Bor79] A. Borel. Automorphic L-functions. Proc. Sympos. Pure Math., XXXIII, pages 27–61. Amer. Math. Soc., Providence, R.I., 1979

[Bor91] Armand Borel. Linear algebraic groups, volume 126 of Graduate Texts in Mathematics. Springer- Verlag, New York, second edition, 1991.

[BH06] Colin J. Bushnell and Guy Henniart. The local Langlands conjecture for GL(2), volume 335, 2006

[FO] Jean-Marc Fontaine and Yi Ouyang, Theory of p-adic Galois Representations, https://www.imo.universite-paris-saclay.fr/~fontaine/galoisrep.pdf

 [GK82]S. S. Gelbart and A. W. Knapp. L-indistinguishability and Rgroups for the special linear group. Adv. in Math., 43(2):101–121, 1982

[HS12] Kaoru Hiraga and Hiroshi Saito. On L-packets for inner forms of SLn. Mem. Amer. Math. Soc., 215(1013):vi+97, 2012.

 [Kud94] Stephen S. Kudla. The local Langlands correspondence: the non-Archimedean case. In Motives (Seattle, WA, 1991), volume 55 of Proc. Sympos. Pure Math., pages 365–391. Amer. Math. Soc., Providence, RI, 1994

[Mur09] Fiona Murnaghan. Representations of reductive p-adic groups. http://www.math.toronto.edu/murnaghan, 2009.

[Spr98] T. A. Springer. Linear algebraic groups, volume 9 of Progress in Mathematics. Birkh ̈auser Boston Inc., Boston, MA, second edition, 1998.

[Tad92] Marko Tadi´c. Notes on representations of non-Archimedean SL(n). Pacific J. Math., 152(2):375–396, 1992

[Wed08] Torsten Wedhorn. The local Langlands correspondence for GL(n) over p-adic fields. In School on Automorphic Forms on GL(n), volume 21 of ICTP Lect. Notes, pages 237–320. Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2008.