Generalized Euler characteristic in power-bounded T-convex valued fields

Abstract

We lay the groundwork in this first installment of a series of papers aimed at developing a theory of Hrushovski-Kazhdan style motivic integration for certain type of non-archimedean o-minimal fields, namely power-bounded T-convex valued fields, and closely related structures. The main result of the present paper is a canonical homomorphism between the Grothendieck semirings of certain categories of definable sets that are associated with the VF-sort and the RV-sort of the language L_TRV. Many aspects of this homomorphism can be described explicitly. Since these categories do not carry volume forms, the formal groupification of the said homomorphism is understood as a universal additive invariant or a generalized Euler characteristic. It admits, not just one, but two specializations to Z. The overall structure of the construction is modeled on that of the original Hrushovski-Kazhdan construction.

This replaces a part of the preprint arXiv:1307.0224. Significant revision and extension (2nd version)

References in corpus (5)

• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Additive invariants in o-minimal valued fields
• Special transformations in algebraically closed valued fields
• Integration in algebraically closed valued fields with sections
• Lipschitz stratifications in power-bounded o-minimal fields

Cited by in corpus (1)

• Non-archimedean stratifications in power bounded $T$-convex fields