Poincaré duality for pro-étale Q_p-local systems

@misc{li2026poincaré,
  title = {{Poincaré duality for pro-étale $\mathbfQ_p$-local systems}},
  author = {Shizhang Li and Wiesława Nizioł and Emanuel Reinecke and Bogdan Zavyalov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.12110},
  eprint = {2609.12110},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.12110},
}

TY  - UNPB
TI  - Poincaré duality for pro-étale Q_p-local systems
AU  - Shizhang Li
AU  - Wiesława Nizioł
AU  - Emanuel Reinecke
AU  - Bogdan Zavyalov
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.12110
UR  - https://arxiv.org/abs/2609.12110
AB  - We prove finiteness and Poincaré duality for pro-étale 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.
ER  -