Generalized Kashiwara conjecture for proper pushforwards
Let be a proper map between schemes over an algebraically closed field, and let be an irreducible -adic perverse sheaf on obtained by the six operations from a one-dimensional local system on a curve . Generalized Kashiwara conjecture. The proper pushforward is semi-simple and satisfies Hard Lefschetz. The source calls this extension of Kashiwara's conjecture very plausible and uses it as an additional expected input concerning perverse sheaves and proper maps. Its status is not resolved in the supplied text.
References
Primary source
A. Braverman and D. Gaitsgory, “Deformations of local systems and Eisenstein series”, arXiv:math/0605139 (2008).
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