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Abstract. We calculate an explicit formula for the topological Hochschild homology of a discrete valuation ring of characteristic zero with finite residue field. From this we deduce the topological Hochschild homology of global number rings.

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We consider the algebraic K-theory of a truncated polynomial algebra in several commuting variables, K.kOEx 1 ;:::;x n =.x a 1 1 ;:::;x a n n //. This naturally leads to a new generalization of the big Witt vectors. If k is a perfect field of positive characteristic we describe the K-theory computation in terms of a cube of these Witt vectors on N n . If the characteristic of k does not divide any of the a i we compute the K-groups explicitly. We also compute the K-groups modulo torsion for k D Z. To understand this K-theory spectrum we use the cyclotomic trace map to topological cyclic homology, and write TC.kOEx 1 ;:::;x n =.x a 1 1 ;:::;x a n n // as the iterated homotopy cofiber of an n-cube of spectra, each of which is easier to understand.

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