Local systems on curves over finite fields and boundedness of trace fields

Event details
Date | 26.10.2022 |
Hour | 14:15 › 16:00 |
Speaker | Josh Lam (Humboldt University, Berlin) |
Location | |
Category | Conferences - Seminars |
Event Language | English |
For a local system on a curve over a finite field, the work of Lafforgue shows that there is a well defined number field, referred to as the trace field, generated by the traces of Frobenius elements at the closed points. A basic question is how do such trace fields vary as the curve and the local system vary. Based on computations of Kontsevich, as well as Maeda's conjecture in the number field setting, one expects that generically such fields are as large as they are allowed to be. I will show that, in the case of rank two local systems, as we vary over all pointed curves of type (g,n) over all finite fields, the set of trace fields of fixed degree is finite. This can be viewed as a uniform (across the moduli of curves) version of a finiteness result of Deligne's in positive characteristic.
Practical information
- Informed public
- Free
Organizer
- Oscak Kivinen
Contact
- Monique Kiener (if you want to attend to the seminar by zoom, please contact me, and I'll give you the link)