Reading group / Groupe de travail

Perverse sheaves

Institut Camille Jordan, July 24-28, 2017.

Schedule

Program

• Talk 0. Lie Fu. Triangulated categories, derived category of constructible sheaves, six operations, Verdier duality.
  Appendix of [dCM] or appendix of [HTT].
• Talk 1.Zhiyu Tian. t-structures. Heart is an abelian category. t-exactness.
  §8.1.1 of [HTT].
• Talk 2. Zhiyu Tian. Recollement.
  §1.4 of [BBD].
• Talk 3 & 4. Lie Fu. Perverse sheaves. The (middle) perversity condition. Properties. Thm 8.1.27 and its proof.
  § 8.1.2 of [HTT].
• Talk 5. Zhiyu Tian. Perverse filtration, perverse cohomology. Examples.
  §2.4-2.6 of [dCM].
• Talk 6 & 7. Zili Zhang. Minimal extension. Two descriptions of minimal extension, their equivalence (Prop 8.2.11), IC complex, simplicity, Intersection homology. If times permits, some examples of computation (Kirwan's book).
  §8.2.1, §8.2.2 of [HTT].
• Talk 8. Stéphane Gaussent. Decomposition theorem (i). Statement and corollaries. Borho-MacPherson's theorem in the semi-small case. Examples of computations.
  §8.2.2 of [HTT].
• Talk 9. Stéphane Gaussent. Applications of decomposition theorem.
  e.g. §4 [dCM]. One can select some topics.
• Talk 10. Zili Zhang. Decomposition theorem (ii). The (Hodge theoretic) proof. Examples of computations.
  §3 of [dCM] or [W].
• Talk 11. ? . Decomposition theorem (iii). The original proof by passing to characteristic p.
  [BBD]

References:

This reading group is supported by the project "Cyles algébriques des variétés de Calabi-Yau et théorie de Hodge" financed by Fédération de Recherche en Mathématiques Rhône-Alpes/Auvergne.