Grothendieck homomorphisms in algebraically closed valued fields III: Fourier transform

Details Grothendieck homomorphisms in algebraically closed valued fields III: Fourier transform Grothendieck homomorphisms in algebraically closed valued fields III: Fourier transform

2009-03-06

arxiv.org/abs/0903.1097v1

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We continue the study of the Hrushovski-Kazhdan integration theory and consider exponential integrals. The Grothendieck ring is enlarged via a tautological additive character and hence can receive such integrals. We then define the Fourier transform in our integration theory and establish some fundamental properties of it. Thereafter a basic theory of distributions (without differential operators) is also developed. We construct the Weil representation in the end as an application. The results are completely parallel to the classical ones.

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