When R is a ring spectrum THH_*(R) is usually not a very nice ring, but calculations of Bokstedt, Ausoni and others show that THH_*(R;k) often has strong duality properties when k is the field with p elements. The purpose of the talk  it so give a non-calculational  proof of this which applies to show more generally that when R--->k is regular and k is of characteristic p then THH(R;k) has Gorenstein duality. (Thanks to Dundas proving my conjectured lemma in February, this is an MSRI theorem).