Time and venue D-3.518, Thursdays 12:30-14:00.
The main reference for the seminar is Mustata's online book.
The chapters below refer to this book.
Tentative programme
Talk 1 (12th September) Introduction and discussion (no formal talk).
Talk 2 (19th September) Riemann's zeta function (Árpád Tóth)
26th September: no talk
Talk 3 (3rd October) Basics of Hasse-Weil zeta functions §2.1-2.4 (Márton Borbényi)
Talk 4 (10th October) Elliptic curves, group law, rational points, examples (Silverman's book "Arithmetic of Elliptic curves §III.1-3, Ádám Sagmeister)
Talk 5 (17th October) Proof of Weil's conjecture for elliptic curves (Silverman's book "Arithmetic of Elliptic curves" §V.1-2, Tamás Szőke)
Talk 6 (24th October) Introduction to (co)homology theories, heuristics on Lefschetz' Fixed Point Theorem
Talk 7 (7th November) Riemann-Roch for curves (Hartshorne: Algebraic geometry, §IV.1, László Koltai)
Talk 8 (14th November) Proof of Weil's conjectures for general smooth curves §3.1-3
Talk 9 (21st November) Estimating exponential sums using Weil's conjectures §6.2-3
Talk 10 (28th November) Grothendieck topologies, sheaf cohomology, étale (\(\ell\)-adic) cohomology §4.3
Talk 11 (5th December) Some \(p\)-adic analysis and Dwork's proof §8 (Narmada Varadarajan)
Talk 12 (12th December) Make-up talk or further topics