Topological cyclic homology of local fields

Abstract: We introduce a new method for computing topological cyclic homology of locally complete intersections over p-adic intergers, by using relative hochschild homology and resolving the base ring spectrum with an Adams reslolution. Using the Nygaard filtration on the E1-term, we can construct algebraic Tate and algebraic homotopy fixed points spectral sequences, which are algebraic and catpture lots of informations in the Tate and homotopy fixed points spectral sequences computing TP and TC^{-1}. Using this method, we can give a uniform way of computing topological cyclic homology of local fields of mixed characteristic.

algebraic topology

Audience: researchers in the topic

MIT topology seminar

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