Cyclic Adams Operations

Michael K. Brown; Claudia Miller; Peder Thompson; Mark E. Walker

doi:10.1016/j.jpaa.2016.12.018

Cyclic Adams Operations

K-Theory and Homology 2019-07-15 v2 Commutative Algebra

Authors: Michael K. Brown , Claudia Miller , Peder Thompson , Mark E. Walker

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Abstract

Let $Q$ be a commutative, Noetherian ring and $Z \subseteq \operatorname{Spec}(Q)$ 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 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.

Cite

@article{arxiv.1601.05072,
  title  = {Cyclic Adams Operations},
  author = {Michael K. Brown and Claudia Miller and Peder Thompson and Mark E. Walker},
  journal= {arXiv preprint arXiv:1601.05072},
  year   = {2019}
}

Comments

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

Cyclic Adams Operations

Abstract

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