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Some recent advances in topological Hochschild homology

2022
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Bulletin of the London Mathematical Society
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We give an account of the construction of the Bhatt-Morrow-Scholze motivic filtration on topological cyclic homology and related invariants, focusing on the case of equal characteristic 𝑝 and the connections to crystalline and de Rham-Witt theory. M S C 2 0 2 0 19D55 (primary), 13D03 (secondary) INTRODUCTION Let 𝑋 be a smooth quasi-projective scheme over a field 𝑘. In this case, one has the algebraic 𝐾theory spectrum 𝐾(𝑋) of 𝑋, defined by Quillen [106] using the exact category of vector bundles

doi:10.1112/blms.12558
fatcat:mudzfrrfgjghfivyvcd4wh4hoi