Timeline for semisimplicity of p-adic Galois representations

6 events

when toggle format	what		by	license	comment
May 14, 2011 at 23:58	vote	accept	A. Pacetti
May 14, 2011 at 23:59
May 14, 2011 at 23:58	comment	added	A. Pacetti		Thanks Matthew for the answer. I was wondering why one cannot generalize the complex case to prove that the p-adic rep's comming from geometry are semisimple. A natural questios was if it happens that all p-adic Galois representations turn out to be semisimple, but we just don't know how to prove it, but by your comment (and David's example) it is clear that this is not the case and there is something deep about etale cohomology.
May 13, 2011 at 14:18	comment	added	LSpice		Err, sorry, I meant $\operatorname{GL}_n(\overline{\mathbb Q_p})$. Of course there is a very literal analogue of Haar measure on $\operatorname{GL}_n(\mathbb Q_p)$. :-)
May 13, 2011 at 3:37	comment	added	LSpice		As has been pointed out, the conclusion is false, so that no analogue of Haar measure can hope to prove it; but there is some analogue of Haar measure on $\operatorname{GL}_n(\mathbb Q_p)$, introduced (I think) by Julia Gordon: math.ca/10.4153/CJM-2006-005-2.
May 13, 2011 at 3:10	history	edited	Emerton	CC BY-SA 3.0	added 219 characters in body
May 13, 2011 at 3:04	history	answered	Emerton	CC BY-SA 3.0