Generalized Kashiwara conjecture for proper pushforwards

Let f:YYf:Y'\to Y” be a proper map between schemes over an algebraically closed field, and let \CF\CF be an irreducible \ell-adic perverse sheaf on YY' obtained by the six operations from a one-dimensional local system on a curve XX. Generalized Kashiwara conjecture. The proper pushforward f!(\CF)f_!(\CF) 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.

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Primary source

A. Braverman and D. Gaitsgory, “Deformations of local systems and Eisenstein series”, arXiv:math/0605139 (2008).

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