turkmath.org

The usual Witt vectors are closely related to p-adic phenomena. The so-called big Witt vectors combine the usual ones for all primes p simultaneously. If one compares this to adele rings, it is natural to ask whether the big Witt vectors exhibit any phenomena related the innite prime (real analysis) such as positivity. It turns out that they do. I'll explain how this lets us extend the big Witt functor to semirings, and I'll discuss the Witt vectors of some classical arithmetic semirings, such as the nonnegative real numbers, the natural numbers, and the Boolean semiring.