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 Break - No talk
July 13 Geometry of Modular Curves over Z_p David Marcil [KM] PDF
July 20 Hasse Invariant Samuel Mundy [KM] PDF
July 27 The Cohomological Correspondence T_p Hung Chiang [BP] PDF
August 3 Classicality mod p Haodong Yao [BP] PDF
August 10 Break - No talk
August 17 Igusa towers and p-adic Theory Avi Zeff [BP] PDF
August 24 More on the Igusa Tower and Duality Jiaxi Mo [K], [BP] PDF
August 31 Break - No talk
September 7 Duality of T_p operators Hung Chiang [BP] PDF
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References
[BP] Boxer, George. Pilloni, Vincent - Higher Hida and Coleman Theories on the Modular Curve
[K] Katz, Nicholas - p-adic L-functions via Moduli of Elliptic Curves
[KM] Katz, Nicholas. Mazur, Barry - Arithmetic Moduli of Elliptic Curves