  This is an account of the algebraic geometry of Witt vectors and arithmetic
jet spaces. The usual, "p-typical" Witt vectors of p-adic schemes of finite
type are already reasonably well understood. The main point here is to
generalize this theory in two ways. We allow not just p-typical Witt vectors
but those taken with respect to any set of primes in any ring of integers in
any global field, for example. This includes the "big" Witt vectors. We also
allow not just p-adic schemes of finite type but arbitrary algebraic spaces
over the ring of integers in the global field. We give similar generalizations
of Buium's formal arithmetic jet functor, which is dual to the Witt functor. We
also give concrete geometric descriptions of Witt spaces and arithmetic jet
spaces and investigate whether a number of standard geometric properties are
preserved by these functors.
