2015/07/26 by Filippo Callegaro, Callegaro, Filippo, Giovanni Gaiffi +3
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.AG #math.AT #math.NT
paper · pdf · doi:10.48550/arxiv.1507.07208
26 pages, added references
openalex publication_date 2015/07/26 · arxiv created 2016/03/10 · arxiv updated 2016/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An important piece of information in the theory of the arithmetic Galois action on the geometric fundamental groups of schemes is that divisorial inertia is acted on cyclotomically. We detail in this note the content of this fact in the case of the profinite braid groups arising from complex reflection groups, naturally viewing them as the geometric fundamental groups of the attending classifying spaces. We also include the case of the full (non colored) braid groups, whose completed classifying spaces are Deligne-Mumford stacks rather than schemes.