Cyclic Adams Operations

Abstract

Let $Q$ be a commutative, Noetherian ring and $Z\subseteq \mathrm{Spec}(Q)$ a closed subset. Define $K_0^Z(Q)$ 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 $K_0^Z(Q)$ and we prove these operations satisfy the four axioms used by Gillet and Soulé 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 Soulé in certain cases.

We have added citations to Olivier Haution's thesis, in which cyclic Adams operations are also developed

Cited by in corpus (2)

• Adams Operations on Matrix Factorizations
• Total Betti numbers of modules of finite projective dimension