Derived completions in stable homotopy theory
Gunnar Carlsson
TL;DR
This paper introduces a new notion of derived completion for homomorphisms of commutative S-algebras, explores its properties, and discusses potential applications in algebraic K-theory.
Contribution
It develops a novel derived completion construction for commutative S-algebras and analyzes its invariance and relationships with existing completion methods.
Findings
Construction of derived completion for commutative S-algebras
Analysis of invariance properties of the construction
Potential applications in algebraic K-theory
Abstract
We construct a notion of derived completion which applies to homomorphisms of commutative S-algebras. We study the relationship of the construction with other constructions of completions, and prove various invariance properties. The construction is expected to have applications within algebraic K-theory.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra