A representation for algebraic K-theory of quasi-coherent modules over affine spectral schemes

2014/11/10 by Ohara, Mariko
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1411.2306

Abstract

In this paper, we study K-theory of spectral schemes by using locally free sheaves. Let us regard the K-theory as a functor K on affine spectral schemes. Then, we prove that the group completion ΩB^G(B^GGL) represents the sheafification of K with respect to Zariski (resp. Nisnevich) topology G, where B^GGL is a classifying space of a colimit of affine spectral schemes GL_n.

Related

• Witt, GW, K-theory of quasi-projective schemes
• Algebraic K-theory of coherent spaces
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• Algebraic Models for Quasi-Coherent Sheaves in Spectral Algebraic Geometry
• Cohomology of coherent sheaves on a proper scheme