PreprintCC BY 4.0arXiv
Local Tate duality for syntomic cohomology in positive characteristic
Abstract
Let k be a local field of characteristic p>0. We show that syntomic cohomology over k, with coefficients, and defined using Dodd's theory of F-gauges, satisfies local Tate duality. We also prove that syntomic cohomology over the ring of integers of k, again with coefficients, is Lagrangian with respect to the duality pairing. Finally, we show that, for p>2, these results recover Shatz's duality and Milne's orthogonality results for the cohomology of finite flat group schemes of p-power order over k.
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BibTeX
@misc{lazda2026local,
title = {{Local Tate duality for syntomic cohomology in positive characteristic}},
author = {Christopher Lazda},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21622},
eprint = {2610.21622},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21622},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local Tate duality for syntomic cohomology in positive characteristic
AU - Christopher Lazda
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21622
UR - https://arxiv.org/abs/2610.21622
AB - Let k be a local field of characteristic p>0. We show that syntomic cohomology over k, with coefficients, and defined using Dodd's theory of F-gauges, satisfies local Tate duality. We also prove that syntomic cohomology over the ring of integers of k, again with coefficients, is Lagrangian with respect to the duality pairing. Finally, we show that, for p>2, these results recover Shatz's duality and Milne's orthogonality results for the cohomology of finite flat group schemes of p-power order over k.
ER -