On the canonical element conjecture

Abstract

The canonical element conjecture is proved in the following two cases: (i) depth A = dim ⁡ A − 1 A = \dim A - 1 , H m n − 1 ( A ) H_m^{n - 1}(A) is decomposable; (ii) depth A = dim ⁡ A − 1 A = \dim A - 1 , H m n − 1 ( A ) ∨ H_m^{n - 1}{(A)^ \vee } is cyclic. The equivalence of the C.E.C. and the improved new intersection theorem is also established.