Special transformations in algebraically closed valued fields
Abstract
We present two of the three major steps in the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan. We limit our attention to a simple major subclass of V-minimal theories of the form ACVF_S(0, 0), that is, the theory of algebraically closed valued fields of pure characteristic expanded by a (VF, Gamma)-generated substructure S in the language L_RV. The main advantage of this subclass is the presence of syntax. It enables us to simplify the arguments with many different technical details while following the major steps of the Hrushovski-Kazhdan theory.
Keywords
Cite
@article{arxiv.1006.2467,
title = {Special transformations in algebraically closed valued fields},
author = {Yimu Yin},
journal= {arXiv preprint arXiv:1006.2467},
year = {2010}
}
Comments
This is the published version of a part of the notes on the Hrushovski-Kazhdan integration theory. To appear in the Annals of Pure and Applied Logic