  We study equivariant de Rham discriminants associated to arithmetic varieties
which support a tame action by a finite group; we form these discriminants by
endowing the de Rham cohomology with pairings arising from duality theory. Such
equivariant discriminants are shown to break up naturally into a metric part
and a signature part. In a previous paper we described the equivariant Arakelov
discriminants, obtained by endowing the equivariant determinant of de Rham
cohomology with various metrics. In this paper we study the associated
equivariant signature information; in particular, we show that the symplectic
signature invariants both determine and are determined by the symplectic
Archimedean epsilon constants of the arithmetic variety.
