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arXiv · 1705.03340

A^1-homotopy invariance in spectral algebraic geometry

Denis-Charles Cisinski·Adeel A. Khan
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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.

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BibTeXRIS

Denis-Charles Cisinski, Adeel A. Khan. 2017-05-09. A^1-homotopy invariance in spectral algebraic geometry. https://arxiv.org/abs/1705.03340

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