2025/11/24 by Hekking, Jeroen, Khan, Adeel A., Rydh, David · 1 citation
Mathematics · #14A30 (Primary) 14A20 #14D23 #14N35 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.48550/arxiv.2511.19412
openalex publication_date 2025/11/24 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28
We develop an analogue of the deformation to the normal cone in the context of derived algebraic geometry. This provides any given morphism of derived stacks with a degeneration to the zero section of its normal bundle (i.e., its 1-shifted relative tangent bundle). The construction is realized via the derived Weil restriction along the zero section of the affine line. We prove a general algebraicity theorem for derived Weil restrictions along finite but possibly non-flat morphisms. As an application of the theory, we study derived blow-ups along arbitrary closed centres, generalizing previous works of the authors in the quasi-smooth case.