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arXiv · 2403.19008

On the algebraizability of formal deformations in $K$-cohomology

Eoin Mackall
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Abstract

We show that algebraizability of the functors $R^1\pi_*\mathcal{K}^M_{2,X}$ and $R^2\pi_*\mathcal{K}^M_{2,X}$ is a stable birational invariant for smooth and proper varieties $\pi:X\rightarrow k$ defined over an algebraic extension $k$ of $\mathbb{Q}$. The same is true for the \'etale sheafifications of these functors as well. To get these results we introduce a notion of relative $K$-homology for schemes of finite type over a finite dimensional, Noetherian, excellent base scheme over a field. We include this material in an appendix.

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Eoin Mackall. 2024-03-27. On the algebraizability of formal deformations in $K$-cohomology. https://arxiv.org/abs/2403.19008

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