  We use chain level genus zero Gromov-Witten theory to associate to any closed
monotone symplectic manifold a formal group (loosely interpreted), whose Lie
algebra is the odd degree cohomology of the manifold (with vanishing bracket).
When taken with coefficients mod p, the p-th power map of the formal group is
related to quantum Steenrod operations. The motivation for this construction
comes from derived Picard groups of Fukaya categories, and from arithmetic
aspects of mirror symmetry.
