Anthony McCormick, Department of Pure Mathematics, University of Waterloo
“The Frobenius Theorem for Supermanifolds Part 2”
We will begin with some basic theory of locally ringed spaces with examples from both differential and algebraic geometry. After introducing the notion of a functor of points we will see a duality between geometric and algebraic objects through the adjunction between the global sections functor and Spec, as well as Milnors exercise in differential geometry. This will motivate the definition of a supermanifold and allow us to better understand the nature of morphisms between them. Using all of this formalism we will then give several examples of supermanifolds, construct the reduced manifold associated to a supermanifold and prove the Frobenius theorem in this more general context.
MC 5501