A1-homotopy invariance in spectral algebraic geometry
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.
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