Abstract
AbstractThe classical Adams operations are defined on the Grothendieck group of algebraic vector bundles on a scheme, and are related to Grothendieck’s Riemann-Roch Theorem. In these notes, I review the theory of Adams operations for Grothendieck groups with supports, following the work of Gillet and Soulé, and give two applications in local algebra: A proof of the Serre Vanishing Conjecture for arbitrary regular local rings (due to Gillet and Soulé) and a proof of the Total Rank Conjecture for many local rings.
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