RELATIVE INVOLUTIVE INVARIANTS OF RINGS

Abstract

Introducing the contents of this thesis is impossible without referring to the fundamental work of A. Verschoren and F. Van Oystaeyen [42], who introduced and studied the theory of relative invariants of commu­ tative rings. One of the fundamental facts on which that theory has been built is that to infer knowledge about the structure of the ring from knowledge about certain invariants. Global invariants like the Picard group or the Brauer group seldom suffice to characterize the base ring, so it is usually necessary to consider more complicated invariants in order to get closer to our goal of obtaining useful structure results for the rings studied. In this thesis we develope an involutive version of the theory of relative invariants, both from an algebraic and a geometric point of ,iew.