Cyclic Adams Operations
Abstract
Let Q be a commutative, Noetherian ring and Z ⊂eq Spec(Q) a closed subset. Define K0Z(Q) to be the Grothendieck group of those bounded complexes of finitely generated projective Q-modules that have homology supported on Z. We develop "cyclic" Adams operations on K0Z(Q) and we prove these operations satisfy the four axioms used by Gillet and Soul\'e in their paper "Intersection Theory Using Adams Operations". From this we recover a shorter proof of Serre's Vanishing Conjecture. We also show our cyclic Adams operations agree with the Adams operations defined by Gillet and Soul\'e in certain cases.
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