Algebraic BP-theory and norm varieties Nobuaki Yagita Department of Mathematics, Faculty of Education, Ibaraki University, Mito, Ibaraki, Japan yagita@mx.ibaraki.ac.jp Primary 14C15, 57T25; Secondary 55R35, 57T05 Let X be a smooth variety over a field k of characteristic zero. For a fixed prime p, the algebraic BP-theory ABP(X) is the algebraic version of the topological BP-theory. Given a nonzero symbol a in K_{n+1}^M (k)/p, the norm variety V_a is a variety such that a=0 in K_{n+1}^M (k(V_a))/p and V_a(C)=v_n. In this paper, we mainly study ABP(V_a) for p an odd prime.