Mod-p Poincare Duality in p-adic analytic geometry

• 成果类型: Article
• 署名作者: Zavyalov, Bogdan
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2025.201.3.2
• 发表日期: 2025
• 页码: 647-773
• 关键词: rigid geometry; COHOMOLOGY; schemes

摘要

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.