Topological Hochschild homology of truncated Brown-Peterson spectra, I

We compute the topological Hochschild homology of sufficiently structured forms of truncated Brown- Peterson spectra with coefficients. In particular, we compute THH*(B(n); * ( B ( n ); H Z (p ) ) for all n , where B ( n ) is an E 3 form of BP(n) ( n ) for certain primes p , and THH*(B(2); * ( B ( 2 ); M ) for M E { k ( 1 ), k ( 2 ) } . For example, this gives a computation of THH(tafD; ( taf D ; M ) for M E { H Z (3) , k ( 1 ), k ( 2 ) } where tafD D is the E1 1 form of BP(2) ( 2 ) constructed by Hill and Lawson.