Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic Fourier transforms over finite fields: generic vanishing,
  convolution, and equidistribution   We study the arithmetic Fourier transforms of trace functions on general
connected commutative algebraic groups. To do so, we first prove a generic
vanishing theorem for twists of perverse sheaves by characters, and 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 then give some concrete examples of applications of
these results and raise a number of questions.

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The categories of this paper are: nlin
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The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph