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Let $K$ be a p-adic local field, $X$ a smooth projective variety over $Spec(K)$, $CH^k(X)$ the Chow group of pure codimension $k$. Then there are cycle maps $cl^X_{DR}:CH^k(X)\to H^{2k}_{DR}(X/K)$ ...

Nowdays, I hear talking about Topological Hochschild Homology more and more often, and I was wondering if someone could point out references to explain why it's important and interesting, and what ...