Complex orientations for THH of some perfectoid fields

Abstract

This sketch argues that work of Hesselholt on the topological Hochschild homology of $\Cp$ extends, using work of Scholze and others, to define complex orientations for a version of topological Hochschild homology for rings of integers in a natural class of generalized cyclotomic perfectoid fields; and that the resulting spectra provide geometrically interesting targets for analogs of the Chern character, defined for certain integral lifts of the extraordinary $K$-functors of chromatic homotopy theory.

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References in corpus (4)

• Integral p-adic Hodge theory
• Completions and derived de Rham cohomology
• Topological Hochschild homology and integral $p$-adic Hodge theory
• $p$-adic geometry