Motivic Poisson summation

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.

46pp

References in corpus (2)

• A motivated introduction to character sheaves and the orbit method for unipotent groups in positive characteristic
• Difference fields and descent in algebraic dynamics - I

Cited by in corpus (5)

• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Fourier transform of the additive group in algebraically closed valued fields
• Integration in algebraically closed valued fields
• Homotopy Spectra and Diophantine Equations
• Integration in algebraically closed valued fields with sections