English

Motivic Poisson summation

Logic 2009-02-06 v1 Algebraic Geometry

Abstract

We develop a "motivic integration" version of the Poisson summation formula for function fields, with values in the Grothendieck ring of definable exponential sums. We also study division algebras over the function field, and obtain relations among the motivic Fourier transforms of a test function at different completions. We use these to prove, in a special case, a motivic version of a theorem of Deligne-Kazhdan-Vigneras.

Keywords

Cite

@article{arxiv.0902.0845,
  title  = {Motivic Poisson summation},
  author = {Ehud Hrushovski and David Kazhdan},
  journal= {arXiv preprint arXiv:0902.0845},
  year   = {2009}
}

Comments

46pp

R2 v1 2026-06-21T12:08:08.662Z