During Summer Term 2022, I and Alvaro Gonzalez Hernandez are running a study group on Hasse-Weil zeta functions. The plan is to study the proofs of the Weil Conjectures for curves and then to get a glimpse of the theory for higher-dimensional varieties. The talks take place in room B3.03 (Zeeman building) on Fridays from 1pm to 2pm.
The planned schedule is as follows.
|Introduction, basic facts and definitions||Óscar Salgado||6th May|
|Rationality and Functional Equation of zeta functions of curves||Elvira Lupoian||13th May|
|Background on Intersection Theory on surfaces||Alvaro Hernandez||20th May|
|The Riemann Hypothesis for curves via Intersection Theory||Steven Groen||27th May|
|The Riemann Hypothesis for curves via the Bombieri-Stepanov method||Phil Holdridge||3rd June|
|Survey of Étale Cohomology and its role in the Weil Conjectures||Arshay Sheth||10th June|
|The Lang-Weil estimates||Sam Chow||17th June|
|Dwork's p-adic proof of rationality of zeta functions, part I||Katerina Santicola||24th June|
|Dwork's p-adic proof of rationality of zeta functions, part II||Nuno Arala||1st July|
- Zeta functions in algebraic geometryLink opens in a new window, by Mircea Mustata
- The Weil Conjectures for curvesLink opens in a new window, by Sam Raskin