Number Theory Seminar - Summer 2021

Higher Hida Theory


Description
Michele Fornea and I organised an online seminar on Higher Hida Theory at Columbia University. We mostly studied the work of Boxer and Pilloni in [BP]. Some topics included (in no particular order) are : modular curves over Z_p, Hasse invariant, cohomological correspondence T_p, Igusa towers, duality results and applications.

The meetings were recorded. Please contact me by e-mail if you wish to see them. E-mail address : dmarcil "at" math.columbia.edu.
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Relevant information
Time: Tuesday, 11:00-12:00 (EST)
Zoom Meeting ID : 949 9700 4653.
Password : Floor(1000e^2)
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Schedule
Date Title Speaker Reference Notes
June 30 Overview of Higher Hida Theory for Modular Curves Michele Fornea [BP] PDF
July 6 No talks
July 13 Geometry of Modular Curves over Z_p David Marcil [KM] PDF
July 20 Hasse Invariant Samuel Mundy [KM]
July 27 (UNOFFICIAL) The Cohomological Correspondence T_p Hung Chiang
August 3 (UNOFFICIAL) Classicality mod p Haodong Yao
August 10 (UNOFFICIAL) Igusa towers and p-adic Theory Avi Zeff
August 17 (UNOFFICIAL) Main Result and Duality Jiaxi Mo
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References
[BP] Boxer, George. Pilloni, Vincent - Higher Hida and Coleman Theories on the Modular Curve
[KM] Katz, Nicholas. Mazur, Barry - Arithmetic Moduli of Elliptic Curves