Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 2048

Preprint Number 2048

Previous Next Preprint server

2048. Artem Chernikov and Alex Mennen
Combinatorial properties of non-archimedean convex sets

Submission date: 9 September 2021


We study combinatorial properties of convex sets over arbitrary valued fields. We demonstrate analogs of some classical results for convex sets over the reals (e.g. the fractional Helly theorem and Bárány's theorem on points in many simplices), along with some additional properties not satisfied by convex sets over the reals, including finite breadth and VC-dimension. These results are deduced from a simple combinatorial description of modules over the valuation ring in a spherically complete valued field.

Mathematics Subject Classification: 52A35, 52A20, 52A01, 12J25

Keywords and phrases:

Full text arXiv 2109.04591: pdf, ps.

Last updated: September 27 2021 16:57 Please send your corrections to: