Submission date: 22 June 2017

Abstract:

Let k be a field of characteristic zero containing all roots of unity and K=k((t)). We build a ring morphism from the Grothendieck group of semi-algebraic sets over K to the Grothendieck group of rigid motives over K, extending the morphism sending the class of an algebraic K-variety to its cohomological motive with compact support. We show that it fits inside a commutative diagram involving Hrushovski and Kazhdan's motivic integration and Ayoub's equivalence between rigid motives over K and quasi-unipotent motives over k; we also show that it satisfy a form of duality. This allows us to answer a question by Ayoub, Ivorra and Sebag about the analytic Milnor fiber.

Mathematics Subject Classification: 14C15, 14F42, 03C60, 14G22, 32S30

Keywords and phrases:

Full text arXiv 1706.07233: pdf, ps.