Additive invariants in o-minimal valued fields

Yimu Yin

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arXiv · 1307.0224

Additive invariants in o-minimal valued fields

Yimu Yin

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Abstract

We develop a theory of Hrushovski-Kazhdan style motivic integration for certain type of non-archimedean o-minimal fields, namely polynomial-bounded T-convex valued fields. The structure of valued fields is expressed through a two-sorted first-order language L_TRV. We establish canonical homomorphisms between the Grothendieck semirings of various categories of definable sets that are associated with the VF-sort and the RV-sort of L_TRV. The groupifications of some of these homomorphisms may be described explicitly and are understood as generalized Euler characteristics. In the end, following the Hrushovski-Loeser method, we construct topological zeta functions associated with (germs of) definable continuous functions in an arbitrary polynomial-bounded o-minimal field and show that they are rational. The overall construction is closely modeled on that of the original Hrushovski-Kazhdan construction, as reproduced in the series of papers by the present author.

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BibTeX RIS

Yimu Yin. 2013-06-30. Additive invariants in o-minimal valued fields. https://arxiv.org/abs/1307.0224

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