Abstract :
Let A subset of B be integral domains with quotient fields F,L resp., L finite separable over F. Suppose that B is integral over A and that A is integrally closed. If βset membership, variantL, we may consider the trace T(β) colon, equals TrLF(β)set membership, variantF. It is classical that, if βset membership, variantB, T(β)set membership, variantA. Viewing elements of B as differential forms of degree 0, we consider here the analogous property when β is a differential form of any degree. We prove that under above assumptions the analogous property indeed holds independently of the degree of the form. The result looks natural, but seems to have never been stated explicitly. We also give a simple geometric application.
