2023/07/19 by Agnieszka Bodzenta, Bodzenta, Agnieszka, Will Donovan +1 · 1 citation
Mathematics · #14C20 #18G80 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 14F08 #Secondary 14A20
paper · pdf · doi:10.48550/arxiv.2307.09888
openalex publication_date 2023/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an effective Cartier divisor D on a scheme X we may form an nth root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and X. We show that this decomposition is 2n-periodic. For n=2 this gives a purely triangulated proof of the existence of a known spherical functor, namely the pushforward along the embedding of D. For n>2 we find a higher spherical functor in the sense of recent work of Dyckerhoff, Kapranov and Schechtman. We use a realization of the root stack construction as a variation of GIT, which may be of independent interest.