Number Theory Seminar - Spring 2022

p-adic Automorphic Forms on Shimura Varieties


Description
I organised a seminar on p-adic automorphic forms on Shimura varieties at Columbia University. The main reference is Hida's book [Hid04] to discuss the theory of Hida families of ordinary forms. Other references, such as papers of Pilloni or Liu-Rosso, are used to discuss the more general theory of P-ordinary forms.
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Relevant information
Time: Wednesday, 4:00pm-5:30pm (Eastern Time)
Room : MATH 507
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Schedule
Date Title Speaker Reference Notes
February 09 GL(2) case David Marcil [Hid04, Ch. 3], [Hid00, 2.5] PDF
February 16 Hilbert-Blumenthal Moduli Haodong Yao [Hid04, Section 4.1] PDF
February 23 Hilbert Modular Shimura Varieties - Part 1 Avi Zeff [Hid04, 4.2.1-4.2.5]
March 02 Hilbert Modular Shimura Varieties - Part 2 David Marcil [Hid04, 4.2.5-4.2.6] PDF
March 09 AWS - No talk
March 16 Spring break - No talk
March 23 Hilbert Modular Shimura Varieties - Part 3 David Marcil [Hid04, 4.2.8-4.2.12 & 4.3]
March 30 Generalized Eichler-Shimura Map Hung Chiang [Hid04, 4.3 & Ch. 5]
April 06 Shimura Varieties Baiqing Zhu [Hid04, Ch. 7]
April 13 Brief Discussion of the Unitary Case David Marcil [CEFMV]
April 20 Ordinary p-adic Automorphic Forms in Unitary Definite Case Yu-Sheng Lee [Hid04, 8.1]
April 27 Unitary Case Continued Yu-Sheng Lee; David Marcil [Hid04, 8.1], [CEFMV]
May 04 Main Theorems Michele Fornea [Hid04, 8.2]
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References
[CEFMV] - CARIAINI et al. - p-adic q-expansion principles on unitary Shimura varieties
[Hid04] - HIDA, Haruzo. p-adic Automorphic Forms on Shimura Varieties
[Hid00] - HIDA, Haruzo. Geometric Modular Forms and Elliptic Curves