Rigid Analytic Geometry
August 27th, 2008 by WaltWikipedia’s article on rigid analytic geometry links to an interesting survey paper by Brian Conrad on the subject. Rigid analytic geometry is the attempt to translate the theory of complex analytic geometry to the p-adics. The theory is surprisingly complicated.
August 28th, 2008 at 7:53 am
broken link
August 28th, 2008 at 10:02 am
Complicated, yes, apparently. “However, even very basic spaces tend to be unwieldy - the projective line over C_p is homeomorphic to an inductive limit of compactifications of affine Bruhat-Tits buildings for PGL(2).”
August 28th, 2008 at 10:42 am
The links are all working for me. Maybe Robbie fixed them.
August 29th, 2008 at 10:32 am
Yeah, I was in the audience for Brian’s talks, and for a p-adic old fart like me, they were both exciting and wonderfully illuminating.
September 1st, 2008 at 3:50 am
I’d be curious about surveys on the applications of rigid geometry in algebraic geometry, e.g. explaining what Raynaud sketched in his ICM 1970 article.
September 1st, 2008 at 8:03 pm
From a worm’s eye view of this very difficult subject, it would be useful for some of us amateurs to see a development of minimal generality, meaning a reduction to the most concrete instances of every component.
To take an example from the intimidating snippet that Jonathan cites, the Coxeter group associated with an affine building occasionally reduces to something as simple as the symmetry group of a regular tiling of the plane, and the prospect of a chain or nesting of similar particularizations gives me some hope that at least one point at the intersection of so many monstrously complicated structures might actually fit in my brain.