Motivic and ℓ-adic realizations of the category of singularities of the zero locus of a global section of a vector bundle

2020/09/28 by Massimo Pippi, Pippi, Massimo
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14B05 #14F08 #14F42 #19E08 #32S30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.13359

openalex publication_date 2020/09/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We study the motivic and ℓ-adic realizations of the dg category of singularities of the zero locus of a global section of a line bundle over a regular scheme. We will then use the formula obtained in this way together with a theorem due to D.~Orlov and J.~Burke - M.~Walker to give a formula for the ℓ-adic realization of the dg category of singularities of the special fiber of a scheme over a regular local ring of dimension n.

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