<p>Recently, Lin and Shinder constructed non-trivial homomorphisms from Cremona groups of rank <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="29_2024_1013_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(&gt;2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="29_2024_1013_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation> using motivic techniques. In this short note we propose an alternative perspective from median geometry on their theorem.</p>

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On a theorem by Lin and Shinder through the lens of median geometry

  • Anthony Genevois,
  • Anne Lonjou,
  • Christian Urech

摘要

Recently, Lin and Shinder constructed non-trivial homomorphisms from Cremona groups of rank \(>2\) > 2 to \(\mathbb {Z}\) Z using motivic techniques. In this short note we propose an alternative perspective from median geometry on their theorem.