Workshop on vanishing cycles and Swan conductors

2023.05.20-2023.05.21, Peking University
Room 1303, Sciences Building No.1 北京大学理科1号楼1303

In this workshop, we aim to study vanishing cycles/topos, local Fourier transform and Gabber-Katz extension in etale cohomology.


Jiangxue Fang
Fangzhou Jin
Enlin Yang
Yigeng Zhao


Tencent Meeting: 777-5318-1470 pw: 235711

09:00-10:00 Vanishing cycles and nearby cycles (Jin)
10:30-11:30 Vanishing topos (Jin)
13:00-14:00 Universally locally acyclicity (Zhao)
14:15-15:15 Universally locally acyclicity (Zhao)
15:30-16:30 Local Fourier transform (Fang)
16:45-17:45 TBA
09:00-10:00 Local Fourier transform (Fang)
10:30-11:30 Local Fourier transform (Fang)
13:00-14:00 Total dimension of vanishing cycles (Yang)
14:15-15:15 Gabber-Katz extension (Yang)

[Abe]T.Abe, Ramification theory from homotopical point of view, I, arXiv:
[Lau87]G.Laumon, Transformation de Fourier, constants d'equations fonctionnelles et conjecture de Weil, Publications mathematiques de l'IHES, tome 65 (1987): 131-210.
[LZ19] Q.Lu and W.Zheng, Duality and nearby cycles over general bases, Duke mathematical journal, Vol.168, No.16, 2019.
[Ill06]Luc Illusie, Vanishing cycles over general bases, after P.Deligne, O.Gabber, G.Laumon and F.Orgogozo,
[Ill15]Luc Illusie, Grothendieck and vanishing cycles,
[Ill17] Luc Illusie, Around the Thom-Sebastiani theorem, with an appendix by Weizhe Zheng, manuscripat math. 152, 61-125(2017).
[Ka-La]N.M.Katz et G.Laumon, Transformation de Fourier et majoration de sommes exponentielles, Publ.Math.IHES, 62 (1985), 361-418.
[Katz86]N.M.Katz, Local-to-global extensions of representations of fundamental groups, Annales de l'institut Fourier, tome 36, n4(1986):69-106.
[Katz87]N.M.Katz, Travaux de Laumon, Seminaire N.Bourbaki, 1987-1988, exp.691, p.105-132.