The Picard group of motivic A(1)

2016/06/16 by Bogdan Gheorghe, Daniel C. Isaksen, Gheorghe, Bogdan +3
Mathematics · #14C22 #14F42 #20G05 #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Element (criminal law) #FOS: Mathematics #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Law #Mathematics #Order (exchange) #Physics #Picard group #Pure mathematics #math.AT #msc:14C22 #msc:14F42 #msc:20G05

paper · pdf · doi:10.48550/arxiv.1606.05191

arxiv created 2016/06/16 · openalex publication_date 2016/06/16 · arxiv updated 2016/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the Picard group Pic(A(1)) of the stable category of modules over ℂ-motivic A(1) is isomorphic to ℤ⁴. By comparison, the Picard group of classical A(1) is ℤ² ⊕ ℤ/2. One extra copy of ℤ arises from the motivic bigrading. The joker is a well-known exotic element of order 2 in the Picard group of classical A(1). The ℂ-motivic joker has infinite order.

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