Group-theoretic Johnson classes and non-hyperelliptic curves with torsion Ceresa class

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 construction to the pro-l etale fundamental groups of smooth curves to obtain Galois-cohomological analogues of these cocycles, which represent what we call the "modified diagonal" and "Johnson" classes, and discuss their relationship to work of Hain and Matsumoto in the case where the curve is proper. We analyze many of the fundamental properties of these classes and use them to give two examples of non-hyperelliptic curves whose Ceresa class has torsion image under the l-adic Abel-Jacobi map.