5. Parity Sheaves and Torsion in IC Sheaves
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Problem 5.1.
[Achar–Williamson]- For which primes p is it true that all indecomposable B-constructible parity \F_p sheaves on G/B are perverse?
- Same question for I-constructible parity \F_p-sheaves on Gr.
(Expect this to be true for large p.) -
Problem 5.2.
[Mautner] For which primes p do the IC sheaves on \operatorname{Perv}_I(Gr, \Z_p) have torsion-free stalks?
(Related to Problem 10.1 part 2, and to Ext-vanishing between reduced standard and costandard modules.) -
Problem 5.3.
[Williamson] Give nontrivial sufficient conditions for indecomposable parity sheaves on G/B or Gr or Fl to be simple perverse sheaves. -
Problem 5.4.
[Achar] Is there a faster algorithm to compute indecomposable parity sheaves on \operatorname{Perv}_{\mathrm{sph}}(Gr, \F_p) than by computing the p-canonical basis?
(Motivated by A. Broer’s algorithm in characteristic 0.)
Cite this as: AimPL: Sheaves and modular representations of reductive groups, available at http://aimpl.org/sheavemodular.