From 7c1d8adfd27e23e48c81939b286820d21f16609d Mon Sep 17 00:00:00 2001 From: Kevin Buzzard Date: Fri, 15 Dec 2023 00:05:25 +0000 Subject: [PATCH] remove final stealth definition --- blueprint/src/chapter/frey.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/blueprint/src/chapter/frey.tex b/blueprint/src/chapter/frey.tex index 41a0d7f2..cdff787d 100644 --- a/blueprint/src/chapter/frey.tex +++ b/blueprint/src/chapter/frey.tex @@ -8,14 +8,14 @@ \section{Hardly ramified representations} We make the following definition (this is not in the literature but it is a useful concept for us). We discuss the meaning of some of the concepts involved afterwards. -\begin{stealthdefinition} Let $p\geq5$ be a prime. A representation $\rho: \GQ\to \GL_2(\Z/p\Z)$ is said to be \emph{hardly ramified} if it satisfies the following four axioms: +\begin{definition} Let $p\geq5$ be a prime. A representation $\rho: \GQ\to \GL_2(\Z/p\Z)$ is said to be \emph{hardly ramified} if it satisfies the following four axioms: \begin{enumerate} \item $\det(\rho)$ is the mod $p$ cyclotomic character; \item $\rho$ is unramified outside $2p$; \item The semisimplification of the restriction of $\rho$ to is unramified. \item The restriction of $\rho$ to $\GQp$ comes from a finite flat group scheme; \end{enumerate} -\end{stealthdefinition} +\end{definition} The theorem we want to discuss in this section is: