2004/03/02 by Ted Chinburg, T. Chinburg, Chinburg, T. +5
Computer Science · Mathematics · #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.math/0403032
46 pages
arxiv created 2004/03/02 · openalex publication_date 2004/03/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.