Mathematical Sciences Research Institute

Home » DDC - Model Theory Seminar: Construction of a structure whose Grothendieck ring has finite characteristic

Seminar

DDC - Model Theory Seminar: Construction of a structure whose Grothendieck ring has finite characteristic December 07, 2020 (08:00 AM PST - 09:00 AM PST)
Parent Program: Decidability, definability and computability in number theory: Part 1 - Virtual Semester MSRI: Online/Virtual
Speaker(s) Esther Elbaz (Fields Institute for Research in Mathematical Sciences)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Video

Construction Of A Structure Whose Grothendieck Ring Has Finite Characteristic

Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

Grothendieck rings were introduced in model theory in the early 2000s. Roughly speaking, to each structure $M$ one associate a ring, called the Grothendieck ring whose elements are (formal differences of) definable sets modulo definable bijection, addition and multiplication reflecting disjoint union and Cartesian product.In this talk, we illustrate general ideas that can be used to construct, given a prechosen ring $R$, a structure that admits $R$ as its Grothendieck ring. We will apply these ideas to the case of $R=\Z[X]/N\Z$.