A^1-homotopy invariance in spectral algebraic geometry

Abstract

We study two different flavours of A^1-homotopy theory in the setting of spectral algebraic geometry, and compare them to classical A^1-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.

47 pages; v2: completely rewritten with a new section on the Bass construction over the sphere spectrum

References in corpus (3)

• Higher Topos Theory
• Cdh descent in equivariant homotopy K-theory
• The Morel-Voevodsky localization theorem in spectral algebraic geometry

Cited by in corpus (4)

• The Morel-Voevodsky localization theorem in spectral algebraic geometry
• K-theory and G-theory of derived algebraic stacks
• Categorical Milnor squares and K-theory of algebraic stacks
• Moduli stack of oriented formal groups and cellular motivic spectra over $\mathbf{C}$