Algebra/Topology seminar – University of Copenhagen

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Algebra/Topology seminar

Thomas Nikolaus, Topological periodic and cyclic homology in non-commutative geometry

Abstract: We will recall the notion of Hochschild homology, topological periodic and cyclic homology for rings and dg-categories. We explain how these concepts are lifts of the algebraic notions of Hochschild and periodic cyclic homology. This relies on ongoing joint work with Peter Scholze about cyclotomic spectra. Then we explain how this perspective leads to finiteness and degeneration results in non-commutative geometry. These results are joint with B. Antieau and A. Mathew.