VALUATIVE CHARACTERIZATION OF CENTRAL EXTENSIONS OF ALGEBRAIC TORI ON KRULL DOMAINS
Let Gbe an affine algebraic group with an algebraic torus over an algebraically closed field Kof an arbitrary characteristic p. We show a criterion for Gto be a finite central extension of in terms of invariant theory of all regular actions of any closed subgroup Hcontaining on affine Krull K-domains such that invariant rational functions are locally fractions of invariant regular functions. Consider a Krull K-domain Rwith a regular action of Hand a prime ideal of Rwith Let denote the inertia group of under the action of H. The group Gis central over if and only if the fraction of ramification indices is equal to or to the p-part of the order of the group of weights of on vanishing on for an arbitrary Rand
Krull domain, ramification index, algebraic group, algebraic torus, character group, invariant theory.