Completion theorem for equivariant $K$-theory

Abstract

In this paper, we study the algebraic analogue of the topological Atiyah-Segal completion theorem. We verify this completion theorem for the algebraic equivariant $K$-theory of smooth projective schemes. We also show that the completion theorem fails in general for smooth non-projective schemes.

Final version, to appear in J. reine angew. Math. (Crelle), (2015)

Cited by in corpus (2)

• Atiyah-Segal Derived Completions for Equivariant Algebraic G-Theory and K-Theory
• Galois descent for completed Algebraic K-theory