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• W3213456427 abstract "We prove a generic vanishing theorem for twists of perverse sheaves on an arbitrary connected commutative algebraic group over a finite field. Using this tool, we construct a tannakian category with convolution as tensor operation. Using Deligne's Riemann Hypothesis, we show how this leads to a general equidistribution theorem for the discrete Fourier transforms of trace functions of perverse sheaves, generalizing the work of Katz in the case of the multiplicative group. We give some concrete examples of applications of these results." @default.
• W3213456427 created "2021-11-22" @default.
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• W3213456427 date "2021-11-15" @default.
• W3213456427 modified "2023-10-03" @default.
• W3213456427 title "Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution." @default.
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• W3213456427 hasPublicationYear "2021" @default.
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