Title: On the Dedekind different of a Cayley-Bacharach scheme,
Abstract: Given a 0-dimensional scheme $\mathbb{X}$ in a projective space
$\mathbb{P}^n_K$ over a field $K$, we characterize the Cayley-Bacharach
property of $\mathbb{X}$ in terms of the algebraic structure of the Dedekind
different of its homogeneous coordinate ring. Moreover, we characterize
Cayley-Bacharach schemes by Dedekind's formula for the conductor and the
complementary module, we study schemes with minimal Dedekind different using
the trace of the complementary module, and we prove various results about
almost Gorenstein and nearly Gorenstein schemes.