比利时vs摩洛哥足彩
,
university of california san diego
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food for thought seminar
dan budreau
ucsd, graduate student
the geometry of schemes (and other tall tales!)
abstract:
this talk will motivate the use of schemes in understanding varieties. schemes are notorious for their lack of transparency. in order to motivate the practicality of schemes, i will discuss the basics of varieties: specifically coordinate rings (the ring you get from a variety) and the various properties that they have. after that, schemes will be (roughly) defined and i will come to the heart of the talk---examples of what happens when we relax various conditions on coordinate rings. very strange phenomena come up: we can get extremely local information, we can get points on varieties with tangent vectors, we can describe some strange varieties over the reals, etc. if time permits, i will talk about schemes as they pertain to number theory and give an example or two. this talk is meant to introduce schemes in a geometric sense. most importantly, i want to brush aside the technical baggage that comes with high-end commutative algebra, sheaves, etc. in order to get at the heart of the geometry. those with a penchant for pictures will be none too displeased.
october 19, 2006
1:00 pm
ap&m 7321
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