Meaning of "p-adic fields" in Jacques Tits' article on classification of semisimple groups

89 Views Asked by At

In Jacques Tits' article "Classification of Algebraic Semisimple Groups", which appears in "Algebraic Groups and Discontinuous Subgroups: Proceedings of Symposia in Pure Mathematics, Volume IX", when on p. 54 he defines the notation $\mathfrak{p}$ to refer to $\mathfrak{p}$-adic fields, does this mean non-archimedean local fields in characteristic zero or non-archimedean local fields in arbitrary characteristic?

On p. 54 he says "$\textbf{F}$ means "finite fields", $\textbf{R}$ "the field of real numbers", $\mathfrak{p}$ "$\mathfrak{p}$-adic fields" ..." and on p. 47 he says "Let $k$ be the field of $\mathfrak{p}$-adic numbers (for some $\mathfrak{p}$)", which suggests he is talking about the characteristic zero case, I guess. No definition of "$\mathfrak{p}$-adic fields" is given anywhere in the text.