(tex) more bestiary ideas for ch5

Author: kbuzzard

blueprint/src/chapter/ch04overview.tex

@@ -50,7 +50,8 @@ \section{Compatible families, and reduction at 3}
 We now use Khare--Wintenberger to lift $\rho$ to a potentially modular $\ell$-adic
 Galois representation of conductor 2, and put it into an $\ell$-adic famiily using
 the Brauer's theorem trick in \cite{blggt}. Finally we look at the 3-adic specialisation
-of this family. Reducing mod 3 we get a representation which must be reducible because
+of this family. Reducing mod 3 we get a representation which is flat at 3 and tame at 2,
+so must be reducible because
 of the techniques introduced in Fontaine's paper on abelian varieties over $\Z$ (an irreducible
 representation would cut out a number field whose discriminant violates the Odlyzko bounds).
 One can now go on to deduce that the 3-adic representation must be reducible, which

blueprint/src/chapter/ch05bestiary.tex

@@ -10,6 +10,10 @@ \chapter{A collection of results which are needed in the proof.}
 
 mult 1, 
 
+cyclic base change
+
+automorphic induction from GL_1(quad extn) to GL_2
+
 Galois rep associated to an auto rep, 
 
 Definition of an automorphic representation for the units of a quaternion algebra over a totally real field (including situations where the algebra is split at one or two infinite places).
@@ -20,4 +24,11 @@ \chapter{A collection of results which are needed in the proof.}
 
 Moret-Bailly
 
-mor to come
+Artin symbol of local class field theory
+
+Existence of solvable extension avoiding a global extension and with prescribed local behaviour
+
+Poitou-Tate
+
+local Tate duality
+