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Mod-p Poincare Duality in p-adic analytic geometry
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DOI：10.4007/annals.2025.201.3.2.png)
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Abstract
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We show Poincare Duality for Fp-etale cohomology of a smooth proper rigid-analytic space over a non-archimedean field K of mixed characteristic (0, p). It positively answers the question raised by P. Scholze in his paper p-adic Hodge theory for rigid-analytic varieties. We prove duality via constructing Faltings' trace map relating Poincare Duality on the generic fiber to (almost) Grothendieck Duality on the mod-p fiber of a formal model. We also formally deduce Poincare Duality for Z/pnZ, Zp, and Qp-coefficients.
Keywords:
rigid-analytic geometry
PoincareDuality
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5.3
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1.4K
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