Let K be a number field with ring of integers OK. Suppose a finite group G acts numerically tamely on a regular scheme X over OK. One can then define a de Rham invariant class in the class group Cl(OK[G]), which is a refined Euler characteristic of the de Rham complex of X. Our results concern the classification of numerically tame actions and the de Rham invariant classes. We first describe how all Galois etale G-covers of a K-variety may be built up from finite Galois extensions of K and from geometric covers. When X is a curve of positive genus, we show that a given etale action of G on X extends to a numerically tame action on a regular model if and only if this is possible on the minimal model. Finally, we characterize the classes in Cl(OK[G]) which are realizable as the de Rham invariants for minimal models of elliptic curves when G has prime order.
This is the author's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.
Glass, Darren B. and Kwon, Sonin, "Galois Structure and De Rhan Invariants of Elliptic Curves" (2009). Math Faculty Publications. 17.
Required Publisher's Statement
Glass, Darren, and Sonin Kwon. Galois Structure and De Rham Invariants of Elliptic Curves. Journal of Number Theory (2009) 129(1):1-14.