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<p>We give a proof of the <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1344_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> <EquationSource Format="TEX">$p$</EquationSource> </InlineEquation>-adic weight-monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze’s proof in the <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="222_2025_1344_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>ℓ</mi> </math></EquationSource> <EquationSource Format="TEX">$\ell $</EquationSource> </InlineEquation>-adic setting, which we adapt using homotopical results developed in the context of rigid analytic motives.</p>

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On the \(p\)-adic weight-monodromy conjecture for complete intersections in toric varieties

  • 期刊论文

  • 发表日期：

    2025年6月17日

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  • Federico Binda,
  • Hiroki Kato,
  • Alberto Vezzani

摘要

We give a proof of the p $p$ -adic weight-monodromy conjecture for scheme-theoretic complete intersections in projective smooth toric varieties. The strategy is based on Scholze’s proof in the ℓ $\ell $ -adic setting, which we adapt using homotopical results developed in the context of rigid analytic motives.