A¹-homotopy invariance in spectral algebraic geometry

2017/05/09 by Denis-Charles Cisinski, Adeel A. Khan, Cisinski, Denis-Charles +1
Mathematics · #14F42 #19E08 #55P43 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1705.03340

openalex publication_date 2017/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study two different flavours of A¹-homotopy theory in the setting of spectral algebraic geometry, and compare them to classical A¹-homotopy theory. As an application we show that the spectral analogue of Weibel's homotopy invariant K-theory collapses to the classical theory. Along the way we give a new construction of nonconnective algebraic K-theory of stable infinity-categories via a generalization of the Bass-Thomason-Trobaugh construction.

Citations

• The six operations in equivariant motivic homotopy theory

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