Applied l-adic Cohomology I - Lecture 4

Explore a lecture from the Ramanujan Lectures series focusing on applied l-adic cohomology, delivered by renowned mathematician Philippe Michel from École polytechnique fédérale de Lausanne. Delve into the fundamental concept of congruence in number theory, first formalized by C.F. Gauss, and discover how trace functions and l-adic cohomology have influenced modern analytic number theory. Learn about the historical developments from Weil's initial studies in the 1940s through Grothendieck's revolutionary contributions to algebraic geometry and étale cohomology, culminating in Deligne's proof of the Riemann Hypothesis for algebraic varieties over finite fields. Examine various examples, including collaborative work with E. Fouvry, E. Kowalski, and W. Sawin, demonstrating the practical applications of these mathematical concepts. Benefit from the expertise of Professor Michel, an accomplished researcher in analytic number theory, whose work spans arithmetic geometry, exponential sums, sieve methods, automorphic forms, L-functions, and ergodic theory.