Speaker :
| Professor Frans Oort (University of Utrecht) |
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Title :
|
Arithmetic and Geometry: Three conjectures about dense sets of points(I) |
Time :
| 2012-12-10 (Mon) 13:30 - 14:10 |
Place : |
Room 202, Astro-Math. Building |
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Abstract: |
Three conjectures will be studied:
Manin-Mumford, Andre-Oort and the Hecke Orbit conjecture.We will show that these statements (in arithmetic algebraic geometry) are very similar: all three study a set of points in an algebraic variety and we ask what the
closure is of this set.
In the first part of my talk I will discuss the basic concepts used: abelian varieties and moduli spaces. I will give examples
and some easy proofs. Some of the aspects will
be illustrated with the theory of elliptic curves. If you want to obtain a general impression about these things, the first
half of the talk will provide this.
In the second part I will discuss some more technical details, and an application. The proof of the Hecke Orbit conjecture is joint work with Ching-Li Chai, using a result by Chia-Fu Yu. |
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