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About: Topological Hochschild homology     Goto   Sponge   NotDistinct   Permalink

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In mathematics, Topological Hochschild homology is a topological refinement of Hochschild homology which rectifies some technical issues with computations in characteristic . For instance, if we consider the -algebra then but if we consider the ring structure on (as a divided power algebra structure) then there is a significant technical issue: if we set , so , and so on, we have from the resolution of as an algebra over , i.e. giving a less pathological theory. Moreover, this calculation forms the basis of many other THH calculations, such as for smooth algebras