Number Theory Seminar

Speaker: Jeffrey Tolliver (John Hopkins U)

Title: The Stefanescu-Viro construction and the universal valuation.

Abstract: Stefanescu and Viro have independently developed a method of constructing hyperfields (which are like fields with a multivalued addition operation) from totally ordered groups. Homomorphisms from a ring into this hyperfield are the same as valuations landing in the corresponding totally ordered group.  On the other hand, Giansiracusa and Giansiracusa have shown that if one allows valuations to take values in idempotent semirings rather than just in totally ordered groups, then each ring has a universal valuation through which other valuations factor uniquely.  I will show how to extend the domains of these two constructions in such a way that they furnish a pair of adjoint functors.