## STNB2018 (32nd edition)

### Universal prevaluations

Xavier Xarles

#### Abstract

I will explain how can extend a bit the notion of valuation (on a ring, or a general semiring) in order to have a universal valuation. This theory of (pre)valuations can then be extended to all Schemes. In order to do this I will explain that there are two posible natural notion of Spec for a semiring and how both notions are related precisely under the universal prevaluation. The talk is elementary, and I will show several examples.