Featured Speaker:  Danielle Wang (MIT)

Title:  Statements of the Weil conjectures, proof for curves via the Hodge index theorem. 

Abstract:  References: Poonen, Rational points on varieties, Chapter 7 up to Section 7.5.1; Milne, The Riemann Hypothesis over Finite Fields: from Weil to the present day, pages 8-10.

The Weil conjectures concern the zeta functions of varieties over a finite field, which for a smooth proper variety are rational functions that satisfy a functional equation and the Riemann hypothesis. The conjectures led to the development of étale cohomology by Grothendieck and Artin. In this talk, we will state the Weil conjectures and prove the Riemann hypothesis for curves using the Hodge index theorem.

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