Ayelet Lindenstrauss

Topological Hochschild homology of number rings

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. AMS Subject Classification: 19D55 (16E40, 19D50, 55T99)

On the Taylor tower of relative K -theory

First published in Geometry & Topology in 16(2), published by Mathematical Sciences Publishers.

The Hochschild homology of fatpoints

This paper calculates the Hochschild homology of fatpoints—rings of the formk[x1,x2,…,xd]/ma wherek is a field of characteristic zero and m=(x1x2,…,xd). The calculation includes the multiplicative structure induced by the shuffle product. The answer is given in terms of the homology of tori relative to theira-diagonal. Since the rings in question are monoidal, this calculation also determines their topological Hochschild homology. By a theorem of Goodwillie, the dimensions of the cyclic homology groups of these rings are determined as well.

TOPOLOGICAL HOCHSCHILD HOMOLOGY AND THE CONDITION OF HOCHSCHILD-KOSTANT-ROSENBERG

*Partially supported by the NSF and the Sloan Foundation. †Partially supported by the Missouri Research Council.