Let Q be a commutative, Noetherian ring and Z⊆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 Soulé in . 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 Soulé in certain cases. Our definition of the cyclic Adams operators is inspired by a formula due to Atiyah . They have also been introduced and studied before by Haution .
ASJC Scopus subject areas
- Algebra and Number Theory