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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.
Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Independent University of Moscow Publisher's website
Journal:
Moscow Mathematical Journal Journal website
Volume:
9
Issue:
3
Pages:
569-623
Publication date:
2009-07-01
Acceptance date:
2008-10-01
EISSN:
1601-3321
Source identifiers:
648776
Keywords:
Pubs id:
pubs:648776
UUID:
uuid:39c4bebd-fb81-4e3f-a337-054349593859
Local pid:
pubs:648776
Deposit date:
2017-01-13

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