University of Kent - Thursday 14th June
There will be a meeting of the COW at the University of Kent, in Canterbury, on Thursday 14th June. The schedule will be as follows.
|1:30pm||Fedor Bogomolov||Torsion Points of Elliptic Curves and Applications to Geometry of Arithmetic Curves|
|4:30pm||Miles Reid||The Tate-Oort Group and Godeaux Surfaces in Mixed Characteristic|
- Fedor Bogomolov (Courant Institute, New York and Higher School of Economics, Moscow) - Torsion Points of Elliptic Curves and Applications to Geometry of Arithmetic Curves
Let E be an elliptic curve over the complex numbers having a standard degree 2 projection E -> P1 to the projective line, with ramification the 2-torsion points of E. I consider the subset P(E) in P1 given as the projection of all the torsion points of E. For two different curves, P(E) and P(E') intersect in a finite set, in many cases in just 1 point.
In the most interesting case when E is defined over a subfield of Qbar, I use an iterative process based on P(E) to construct a nontrivial infinite algebraic extension of the field Q(j(E)), where j(E) is the j-invariant of E, which depends on Q(j(E)) and is strictly smaller than Qbar.
I consider some applications of results on the properties of the P(E) and their subsets to construction of unramified correspondences between curves of higher genus defined over arithmetic and finite fields. Compare arXiv:1706.01586.
- Sara Filippini (Imperial) - TBA
- Abstract fortcoming.
- Miles Reid (Warwick) - The Tate-Oort Group and Godeaux Surfaces in Mixed Characteristic
- Abstract forthcoming.
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