Borel's rank theorem for Artin L-functions.

Borel's rank theorem identifies the ranks of algebraic K-groups of the ring of integers of a number field with the orders of vanishing of the Dedekind zeta function attached to the field. Following the work of Gross, we establish a version of this theorem for Artin L-functions by considering equivariant algebraic K-groups of number fields with coefficients in rational Galois representations. This construction involves twisting algebraic K-theory spectra with rational equivariant Moore spectra. We further discuss integral equivariant Moore spectra attached to Galois representations and their potential applications in L-functions. [ABSTRACT FROM AUTHOR]