Algebra Seminar series July-Dec 2019: Weil Conjectures
The talks will take place on Mondays at 11:30 to 1:00. The first two talk will be on an overview (and some history) of the conjecture. The next few talks will cover etale cohomology, Lefschetz fixed theorem, rationality and the functional equation of the zeta function.
For the Riemann hypothesis part, we will follow Nicholas Katz's simplification ([Katz]) of Deligne's second proof of the conjecture (which appeared in [Weil II]).
Below is the schedule for the first few talks.
Reference(s):
[Katz] N. Katz, L-Functions and Monodromy: Four Lectures on Weil II.
[Weil II] P. Deligne, La conjecture de Weil II, Pub. Math. I.H.E.S., 52 (1981), pp. 313-428.
R. Hartshorne, Algebraic Geometry, book Appendix on Weil conjectures.
J. Milne, Etale cohomology, book.
Schedule
29/07/19; Jishnu Biswas; Overview of Weil conjectures
05/08/19; Jishnu Biswas; Overview of Weil conjectures (contd.)
The above two talks were based on V. Srinivas's expository article on the Weil conjectures.
19/08/19; Ramesh Sreekantan; Counting solutions of equations over finite fields.
26/08/19; Ramesh Sreekantan; Proof of Weil conjectures for hypersurfaces.
The talks by Ramesh were based on a book by Ireland and Rosen.
6/08/19; Bharat Sethuraman; Etale site and sheaves on them
13/09/19; Bharat Sethuraman; Etale cohomology
16/09/19; Bharat Sethuraman; Some results on etale cohomology
23/09/19;Shreedhar Inamdar; On Lefschetz fixed point theorem
30/09/19;Shreedhar Inamdar; On Lefschetz fixed point theorem
11/10/19;Shreedhar Inamdar; Proof of rationality and functional equation
14/10/19;Soumyadip Das; On etale fundamental group
21/10/19;Soumyadip Das; On etale fundamental group
04/11/19;Jishnu Biswas; Fundamental theorems in etale cohomology
7/11/19;Jishnu Biswas; Fundamental theorems in etale cohomology
18/11/19;Jishnu Biswas; Fundamental theorems in etale cohomology
22/11/19;Jishnu Biswa; Fundamental theorems in etale cohomology
25/11/19;Jishnu Biswa; Fundamental theorems in etale cohomology
/11/19; Manish Kumar; On l-adic sheaves