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