arXiv subjects
Publications and source records attributed to Yoav Yaffe.
Let $(K,ν)$ be a real closed valued field, and let $S\subseteq K^n$ be a definable open semi-algebraic set. We find an algebraic characterization of rational functions which are OVF-integral on $S$. We apply the existing model theoretic framework for proving ganzstellensätze, and need to control semi-sections and their relations to orderings. (joint work with Noa Lavi)
When $R$ is a non-archimedean real closed field we say that a function $f\in R(\bar{X})$ is finitary at a point $\bar{b}\in R^n$ if on some neighborhood of $\bar{b}$ the defined values of $f$ are in the finite part of $R$. In this note we give a characterization of rational functions which are finitary on a set defined by positivity and finiteness conditions. The main novel ingredient is a proof that OVF-integrality has a natural topological definition, which allows us to apply a known Ganzstellensatz for the relevant valuation. We also give some information about the Kochen geometry associated with OVF-integrality.
Version 1 of this paper (arXiv:1010.2709v1) was submitted exclusively by Noa Lavi, without prior knowledge, let alone consent, by Yoav Yaffe. Yoav Yaffe is {\em not} an author of any version of this paper, with the exception of the present clarification.
This is an attempt at an elementary exposition, with examples, of the theory of motivic integration developed by R. Cluckers and F. Loeser, with the view towards applications in representation theory of p-adic groups.