发表机构
Morningside Center of Mathematics and State Key Laboratory of Mathematics Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; CNRS, IMJ-PRG, Sorbonne Université; Institut for Matematiske Fag, Københavns Universitet; University of Maryland, Department of Mathematics（中国科学院数学与系统科学研究院，中国科学院数学与系统科学研究所; 法国国家科学研究中心，IMJ-PRG，索邦大学; 哥本哈根大学数学系; 马里兰大学，数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在Banach-Colmez空间框架下证明了真p-adic刚性解析空间上pro-étale Q_p-局部系的有限性、庞加莱对偶及最优上同调消失界，并推广至算术上同调。
AI 中文摘要
我们在Banach-Colmez空间的框架下，证明了真$p$-进刚性解析空间上pro-étale $\mathbf{Q}_p$-局部系的有限性和庞加莱对偶，并建立了其最优上同调消失界。作为推论，我们还获得了其算术pro-étale上同调的普通有限性和对偶性。我们将这些结果从Fargues-Fontaine曲线上完美复形的相应结果推导出来，而后者又归结为周期环上完美复形的庞加莱对偶。我们通过与我们先前有限系数工作中相同的图解论证，给出了后一对偶性的简单证明。在此过程中，我们建立了仿射完美空间上某些周期环的完美复形的最优$v$-下降。
英文摘要
We prove finiteness and Poincaré duality for pro-étale $\mathbf{Q}_p$-local systems on proper $p$-adic rigid-analytic spaces in the framework of Banach--Colmez spaces and establish their optimal cohomological vanishing bounds. As a consequence, we also obtain ordinary finiteness and duality for their arithmetic pro-étale cohomology. We deduce these results from their analogs for perfect complexes on the Fargues--Fontaine curve, which in turn reduce to Poincaré duality for perfect complexes over period rings. We give a simple proof of the latter duality via the same diagrammatic argument as in our previous work for finite coefficients. Along the way, we establish optimal $v$-descent for perfect complexes over certain period rings on affinoid perfectoid spaces.
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