# TOPOLOGY ON COHOMOLOGY OF LOCAL FIELDS

@article{Cesnavicius2015TOPOLOGYOC,
title={TOPOLOGY ON COHOMOLOGY OF LOCAL FIELDS},
author={Kestutis Cesnavicius},
journal={Forum of Mathematics, Sigma},
year={2015},
volume={3}
}
Arithmetic duality theorems over a local field $k$ are delicate to prove if $\text{char}\,k>0$. In this case, the proofs often exploit topologies carried by the cohomology groups $H^{n}(k,G)$ for commutative finite type $k$-group schemes $G$. These ‘Čech topologies’, defined using Čech cohomology, are impractical due to the lack of proofs of their basic properties, such as continuity of connecting maps in long exact sequences. We propose another way to topologize $H^{n}(k,G)$: in the key case… Expand
12 Citations
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