Abstract: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 … Show more
We exhibit a non-hyperelliptic curve $C$ of genus $3$ such that the class of the Ceresa cycle $[C]-[C^-]$ in $JC$ modulo algebraic equivalence is torsion.
We exhibit a non-hyperelliptic curve $C$ of genus $3$ such that the class of the Ceresa cycle $[C]-[C^-]$ in $JC$ modulo algebraic equivalence is torsion.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.