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<p>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.</p>

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Virtual Motives for Synthetic Geometries, A. Definition and Properties of \(K_0(\mathcal {Q}_\ell )\)

  • 期刊论文

  • 发表日期：

    2025年5月22日

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  • Koen Thas

摘要

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.