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<p>We study the module of universal norms associated with a de Rham <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3131_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> </InlineEquation>-adic Galois representation in a perfectoid field extension. In particular, we compute precisely this module when the Hodge–Tate weights of the representation are greater than or equal to <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3131_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. This generalises a result by Coates and Greenberg for abelian varieties, and partially answers a question of theirs. Our method relies on the classification of vector bundles over the Fargues–Fontaine curve.</p>

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Universal norms and the Fargues–Fontaine curve

  • 期刊论文

  • 发表日期：

    2025年4月26日

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  • Gautier Ponsinet

摘要

We study the module of universal norms associated with a de Rham \(p\) p -adic Galois representation in a perfectoid field extension. In particular, we compute precisely this module when the Hodge–Tate weights of the representation are greater than or equal to \(0\) 0 . This generalises a result by Coates and Greenberg for abelian varieties, and partially answers a question of theirs. Our method relies on the classification of vector bundles over the Fargues–Fontaine curve.