Fourier transform of the additive group in algebraically closed valued fields
Logic
2014-03-25 v3 Algebraic Geometry
Abstract
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 is also developed. We construct the Weil representations in the end as an application. The results are completely parallel to the classical ones.
Cite
@article{arxiv.0903.1097,
title = {Fourier transform of the additive group in algebraically closed valued fields},
author = {Yimu Yin},
journal= {arXiv preprint arXiv:0903.1097},
year = {2014}
}