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<p>We compute, via the <i>p</i>-adic Langlands correspondence, the semisimplifications of the mod-<i>p</i> reductions of 2-dimensional crystalline representations of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1092_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="85" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\,\textrm{Gal}\,}}(\overline{\mathbb {Q}}_p/{\mathbb {Q}}_p)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow> <mspace width="0.166667em" /> <mtext>Gal</mtext> <mspace width="0.166667em" /> </mrow> <mo stretchy="false">(</mo> <msub> <mover> <mi mathvariant="double-struck">Q</mi> <mo>¯</mo> </mover> <mi>p</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi mathvariant="double-struck">Q</mi> <mi>p</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> of slope (2,&#xa0;3).</p>

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Reductions of modular Galois representations of slope (2,3)

  • 期刊论文

  • 发表日期：

    2025年5月26日

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  • Enno Nagel,
  • Aftab Pande

摘要

We compute, via the p-adic Langlands correspondence, the semisimplifications of the mod-p reductions of 2-dimensional crystalline representations of \({{\,\textrm{Gal}\,}}(\overline{\mathbb {Q}}_p/{\mathbb {Q}}_p)\) Gal ( Q ¯ p / Q p ) of slope (2, 3).