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arXiv · 1601.05072

Cyclic Adams Operations

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.

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Michael K. Brown, Claudia Miller, Peder Thompson, Mark E. Walker. 2016-01-19. Cyclic Adams Operations. https://doi.org/10.1016/j.jpaa.2016.12.018

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