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Local Tate duality for syntomic cohomology in positive characteristic
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
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