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 Faergeman, Kenta Suzuki
When? Wednesdays 3:00-4:30PM, Fine Hall 1201

Schedule

September 9 (Joakim). Organization and Introduction

Sheaves on real manifolds

September 16. Derived categories of sheaves
September 23. Six functors, nearby and vanishing cycles, and Fourier-Sato transform
September 30. Definition of singular support and basic properties
October 7. Characteristic cycles

Sheaves on complex manifolds

October 14. \(\mathbb C\)-constructible sheaves and holomorphic nearby cycles
October 21. Fall Recess -- no meeting!
October 28. Singular support via holomorphic nearby cycles

\(\ell\)-adic sheaves

November 4. Sheaves on sites, \(\ell\)-adic sheaves, and six functors
November 11. Constructible sheaves are holonomic
November 18. The characteristic cycle and singular support of \(\ell\)-adic sheaves
November 25. Thanksgiving Recess -- no meeting!
December 2. Saito's index formula
December 9. the Grothendieck-Ogg-Shafarevich formula, and applications

References

Main References

M. Kashiwara and P. Schapira, Sheaves on Manifolds, link
A. Beilinson, Constructible sheaves are holonomic, link
T. Saito, The characteristic cycle and the singular support of a constructible sheaf, link