Algebraic K-groups as Galois modules

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This volume originated from a graduate course at the Fields Institute in Autumn 1993, part of a program titled "Artin L-functions." The final chapter introduced a method to construct class-group valued invariants from Galois actions on algebraic K-groups in dimensions two and three of number rings, inspired by Chinburg invariants that pertain to dimensions zero and one. The classical Chinburg invariants assess the Galois structure of classical objects like units in rings of algebraic integers. During the "Galois Module Structure" workshop in February 1994, discussions following my lecture on my invariant (0,1 (L/K, 3) from Chapter 5) revealed that similar higher-dimensional cohomological and motivic invariants were emerging in the work of various authors. Motivated by this development and believing that K-theory represents a fundamental motivic cohomology theory, I embraced the chance to collaborate on computing and generalizing these K-theoretic invariants. These generalizations took various forms—both local and global—as I engaged with aspects of number theory and the ongoing trends in arithmetic geometry related to "Galois Module Structure."