Student Seminar: Number Theory and Automorphic Forms

Organizers: Lior Silberman, Julia Gordon.

Contact: lior @ math.ubc.ca MATH 229B 604-827-3031

Fall 2016: Counting points on varieties over finite fields

We will discuss the problem of estimating the number of mod-p solutions to a system of polynomial equations. Our main reference is [2] below.


Agenda

Section references are to [2] unless noted otherwise.

Meeting Title Speaker Notes & References
1. 14/9 Introduction Myrto Mavraki §1, notes
2. 21/9 (some) Algebraic Geometry Ed Belk §§2.1-2.2
3. 28/9 The Riemann--Roch Theorem Avi Kulkarni §3.0, [1]
4. 5/10 Calculations with power series Thomas Rud §§2.3-2.6
5. 19/10 Proof of Weil's Theorem Myrto Mavraki §§3.1-3.3, notes
5. 26/10 TBA Abhishek Shukla  

References

Topics Author(s) Title Data
[1] Marc Hindry and Joe Silverman Diophantine geometry GTM-201, Springer, 2000
[2] Mircea Mustaţă Zeta functions in algebraic geometry (notes from a 2011 course)


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Last modified: Tuesday October 25, 2016