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Mathematics > Algebraic Geometry

arXiv:1805.04942 (math)
[Submitted on 13 May 2018]

Title:Motivic volume of families of polarized rigid-analytic tori

Authors:Dmitry Sustretov
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Abstract:Let $k$ be a non-Archimedean rational valued field. We construct the moduli space of linearly rigidified polarized analytic tori over $k$ that admit rigid-analytic uniformization by an algebraic torus and observe that it is in definable rigid subanalytic bijection with a $PGL_N$-bundle over a polyhedral domain in an algebraic torus. We use this observation to prove that the Hrushovski-Kazhdan motivic volume of a non-Archimedean semi-algebraic family of Abelian varieties admitting such a uniformization fibrewise vanishes. This question is motivated by the conjectural geometric interpretation of tropical refined multiplicities of Block and Goetsche proposed by Nicaise, Payne and Schroeter.
Comments: comments welcome
Subjects: Algebraic Geometry (math.AG); Logic (math.LO)
Cite as: arXiv:1805.04942 [math.AG]
  (or arXiv:1805.04942v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.04942

Submission history

From: Dmitry Sustretov [view email]
[v1] Sun, 13 May 2018 20:44:37 UTC (14 KB)
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