Virtual motives for synthetic geometries, A. Definition and properties of $K_0({\mathcal{Q}}_{\ell })$

Abstract

In this note, we introduce the first basics on Grothendieck rings for incidence geometries as a new motivic way and tool to study synthetic geometry. In this first instance, we concentrate on generalized quadrangles and related geometries. Many questions, new properties and insights arise along the way.

56 pages; submitted (October 2021)