Abstract
The ‘Equivariant Tamagawa Number Conjecture’ formulated by Flach and the present author is a natural refinement of the seminal Tamagawa Number Conjecture that was originally formulated by Bloch and Kato and then subsequently extended and refined by Kato and by Fontaine and Perrin-Riou. We explain how the additional information implicit in this refinement entails a variety of explicit predictions concerning both the leading terms and values of equivariant motivic L-functions and the module structure of integral motivic cohomology groups. We also discuss several concrete applications of this approach in the setting of Artin and Hasse-Weil L-functions.
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