2014/06/09 by J. P. C. Greenlees, Greenlees, J. P. C.
Mathematics · #13D03 #13D45 #13H10 #19D55 #55P43 #55P50 #55U30 #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AC #math.AT #math.KT #msc:13D03 #msc:13D45 #msc:13H10 #msc:19D55 #msc:55P43 #msc:55P50 #msc:55U30
paper · pdf · doi:10.48550/arxiv.1406.2162
Improved organization of examples, additional details and references
arxiv created 2015/07/17 · arxiv updated 2015/07/20
We consider the Gorenstein condition for topological Hochschild homology, and show that it holds remarkably often. More precisely, if R is a commutative ring spectrum and and R----->k is a ring map to a field of characteristic p then, provided k is small as an R-module, THH(R;k) is Gorenstein in the sense of Dwyer-Greenlees-Iyengar. In particular, this holds if R is a (conventional) regular local ring with residue field k of characteristic p. Using only Bokstedt's calculation of THH(k), this gives a non-calculational proof of dualities observed in calculations by Bokstedt, McClure-Staffeldt, Ausoni-Rognes, Ausoni, Lindenstrauss-Madsen, Angeltweit-Rognes and others. A lemma of Dundas shows that THH(R;k) is remarkably computable.