Timeline for Unitary groups over number fields

7 events

when toggle format	what		by	license	comment
May 2, 2011 at 19:13	vote	accept	Neal Harris
May 2, 2011 at 2:47	comment	added	Kimball		From a representation theoretic point of view (in automorphic forms), you don't need to, and most papers I look at (not that I look at unitary groups often) don't require this. E.g., see Gross-Gan-Prasad: math.ucsd.edu/~wgan/work8-3.pdf.
May 1, 2011 at 21:40	answer	added	Emerton		timeline score: 11
May 1, 2011 at 20:44	answer	added	Jon Yard		timeline score: 13
Apr 13, 2011 at 19:37	comment	added	Mikhail Borovoi		If you take $F$ to be totally real and $F$ CM, i.e. a totally imaginary quadratic extension of $F$, then the restriction of scalars $G:=R_{F/\mathbb{Q}} \mathrm{SU}(V)$ is a group of Hermitian type, i.e. it acts on a Hermitian symmetric domain $X$. If you choose a congruence subgroup $\Gamma\subset G(\mathbb{Q})$, then $X/\Gamma$ is a Shimura variety.
Apr 13, 2011 at 19:32	comment	added	Kevin Buzzard		When working with automorphic representations, you're in good shape if the representations show up in the cohomology of a Shimura variety that satisfies Deligne's axioms. Not every connected reductive group gives rise to such a situation---but if $F$ is totally real and $E$ CM then this is one of the cases where everything works. Because of this you can attach Galois representations to certain automorphic forms on these groups. If Deligne's axioms fail you may not know where to start.
Apr 13, 2011 at 19:10	history	asked	Neal Harris	CC BY-SA 3.0