2016/10/11 by Nicolas Ricka, Ricka, Nicolas
Mathematics · #18E30 #19L41 #20J05 #55P42 #55S10 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18E30 #msc:19L41 #msc:20J05 #msc:55P42 #msc:55S10
paper · pdf · doi:10.48550/arxiv.1610.03561
23 pages, all comments are welcome, v2 fixed some typos
openalex publication_date 2016/10/11 · arxiv created 2016/10/19 · arxiv updated 2016/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the particular properties of the stable category of modules over a finite dimensional cocommutative graded connected Hopf algebra A, via tensor-triangulated geometry. This study requires some mild conditions on the Hopf algebra A under consideration (satisfied for example by all finite sub-Hopf-algebras of the modulo 2 Steenrod algebra). In particular, we study some particular covers of its spectrum of prime ideals Spc(A), which are related to Margolis' Work. We then exploit the existence of Margolis' Postnikov towers in this situation to show that the localization at an open subset U of Spc(A), for various U, assembles in an ∞-stack. Finally, we turn to applications in the study of Picard groups of Hopf algebras and localizations in the stable categories of modules.