Dean Bisogno ; Wanlin Li ; Daniel Litt ; Padmavathi Srinivasan - Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class

epiga:6849 - Épijournal de Géométrie Algébrique, March 30, 2023, Volume 7 - https://doi.org/10.46298/epiga.2023.volume7.6849
Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa classArticle

Authors: Dean Bisogno ; Wanlin Li ; Daniel Litt ; Padmavathi Srinivasan

    Let l be a prime and G a pro-l group with torsion-free abelianization. We produce group-theoretic analogues of the Johnson/Morita cocycle for G -- in the case of surface groups, these cocycles appear to refine existing constructions when l=2. We apply this to the pro-l etale fundamental groups of smooth curves to obtain Galois-cohomological analogues, and discuss their relationship to work of Hain and Matsumoto in the case the curve is proper. We analyze many of the fundamental properties of these classes and use them to give an example of a non-hyperelliptic curve whose Ceresa class has torsion image under the l-adic Abel-Jacobi map.


    Volume: Volume 7
    Published on: March 30, 2023
    Accepted on: November 21, 2022
    Submitted on: October 21, 2020
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Geometric Topology,Mathematics - Number Theory,2010. 14C25, 14F20, 14F30, 14F35, 14G32, 14H45
    Funding:
      Source : OpenAIRE Graph
    • Anabelian Methods in Arithmetic and Algebraic Geometry; Funder: National Science Foundation; Code: 2001196

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