# What is meant by a mixed characteristic field?

I noticed that in a lecture at the IHES, Peter Scholze seemed to refer to a "mixed-characteristic field". Now, I know what a mixed characteristic ring is – it's a ring $A$ such that the localizations at primes $\kappa(\mathfrak{p})$ vary from being characteristic $0$ to being characteristic $p>0$. However, with this definition, it makes no sense to talk about a "mixed-characteristic field".

It seems like he is considering something of the sort $\mathbb{Q}_p(x)$ to be a mixed characteristic field, but I really can't see any intrinsic property of a field that fits the idea of "mixed-characteristic".

• It's basically a field which maintains itself characteristic 0, while its quotient ring has a positive characteristic – enedil Apr 24 '17 at 23:18
• You might want to read Scholze's answer detailing some of fis research: mathoverflow.net/a/66563/62132 – enedil Apr 24 '17 at 23:24