On higher topological Hochschild homology of rings of integers

TL;DR

This paper computes higher topological Hochschild homology of rings of integers in number fields using iterative and homological algebra techniques, extending known results from ordinary THH.

Contribution

It provides a new method to calculate higher THH of rings of integers, reducing complex computations to homological algebra starting from established THH results.

Findings

Explicit calculations of higher THH for rings of integers in number fields.

Reduction of higher THH computations to homological algebra.

Extension of Bökstedt and Lindenstrauss-Madsen results to higher THH.

Abstract

We determine higher topological Hochschild homology of rings of integers in number fields with coefficients in suitable residue fields. We use the iterative description of higher THH for this and Postnikov arguments that allow us to reduce the necessary computations to calculations in homological algebra, starting from the results of B\"okstedt and Lindenstrauss-Madsen on (ordinary) topological Hochschild homology.