Seminar on Singular Support
The goal is to define the singular support of \(\ell\)-adic sheaves, explore its basic properties, and (time-admitting) give applications.Organizers: Joakim Færgeman, Kenta Suzuki
When? Wednesdays 3:10-4:40PM, Fine Hall 1201
Schedule
- September 9 (Joakim). Organization and Introduction Notes
- September 16 (Xiaoyu). Derived categories of sheaves
- September 23 (Paweł). Six functors, nearby and vanishing cycles, and Fourier-Sato transform
- September 30 (Xingzhu). Definition of singular support and basic properties Note the special time: 2:30–4:00PM, because of the annual reception.
- October 7 (Sam). \(\mathbb C\)-constructible sheaves and holomorphic nearby cycles
- October 14 (Meenakshi). Singular support is Lagrangian, and characteristic cycles
- October 21. Fall Recess -- no meeting!
- October 28. Index formula
- November 4 (Dhruv). Sheaves on sites, \(\ell\)-adic sheaves, and six functors
- November 11 (Quanlin). Definition of singular support à la Beilinson
- November 18. Properties of the singular support of \(\ell\)-adic sheaves
- November 25. Thanksgiving Recess -- no meeting!
- December 2. Characteristic cycles and Saito's index formula
- December 9. the Grothendieck-Ogg-Shafarevich formula, and applications
References
Generalities on sheaves- G. Williamson, An Illustrated Guide to Perverse Sheaves, link
- M. Goresky, Lectures Notes on Sheaves and Perverse Sheaves, link
- D. Gaitsgory and J. Lurie, Weil's conjecture for function fields, Section 4, link
- L. Maxim, Notes on vanishing cycles and applications, link