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Notes from the Arbeitsgemeinschaft 2017: Higher Gross-Zagier Formulas

This page contains notes I took during 2017 Arbeitsgemeinschaft on Higher Gross-Zagier Formulas in Oberwolfach. I have edited the notes somewhat, possibly introducing errors.

Here is everything in one file.

Day 1

An overview of the Gross-Zagier and Waldspurger formulas (Yunqing Tang)
The stacks \Bun_n and Hecke (Timo Richarz)
Moduli of Shtukas (I) (Doug Ulmer)
Moduli of Shtukas (II) (Brian Smithling)

Day 2

Automorphic forms over function fields (Ye Tian)
The work of Drinfeld (Arthur Cesar le Bras)
Analytic RTF: the geometric side (Jingwei Xiao)
Analytic RTF: the spectral side (Ilya Khayutin)

Day 3

Definition of N_d; geometric interpretation of orbital integrals. (Yihang Zhu)
Definition and properties of Md (Jochen Heinloth)

Day 4

Intersection theory on stacks (Michael Rapoport)
LTF for cohomological correspondences (Davesh Maulik)
Definition and description of Hk_{M,d}^{\mu}; Expressing I(h_D) as a trace (Liang Xiao)
Alternative calculation of I_r(h_D) (Yakov Varshavsky)

Day 5

Comparison of M_d and N_d; the weight factors (Ana Caraiani)
Horocycles (Lizao Ye)
Cohomological spectral decomposition; finish the proof (Chao Li). Please see Chao's official writeup, which is more complete and correct.

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Notes from the Arbeitsgemeinschaft 2017: Higher Gross-Zagier Formulas