On the algebraizability of formal deformations in K-cohomology

2024/03/27 by Eoin Mackall, Mackall, Eoin
Mathematics · #14C35 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2403.19008

openalex publication_date 2024/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that algebraizability of the functors R¹π_*K^M_2,X and R²π_*K^M_2,X is a stable birational invariant for smooth and proper varieties π:X→ k defined over an algebraic extension k of ℚ. The same is true for the étale 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.

Related

• Operads, Grothendieck topologies and Deformation theory
• Stable birational invariants with Galois descent and differential forms
• Extension of functors for algebras of formal deformation
• Universal birational invariants and \mathbbA¹-homology
• Deformations of homotopy algebras