Séminaire des jeunes : Davide Ricci (LMV) : Some ideas on étale and ℓ-adic cohomology
Séminaire des jeunes : Davide Ricci (LMV) : Some ideas on étale and ℓ-adic cohomology
8 avril / 16:30 - 17:30
La prochaine séance du séminaire des jeunes aura lieu le mardi 8 Avril de 16h30 à 17h30 dans la salle de séminaires du laboratoire.
L’orateur sera Davide Ricci, doctorant en première année de thése dans l’équipe Algèbre et Géometrie.
Some ideas on étale and ℓ-adic cohomology
During the last century, the Weil conjectures motivated the need for new cohomology theories for algebraic varieties over positive characteristic fields. The desired “good” properties are summarized in the Weil cohomology theory axioms. In the sixties, Grothendieck established the foundations of étale cohomology, with Artin and Serre, and later ℓ-adic cohomology, which provides the first example of such a theory. This is not the only one known nowadays, but it is still studied and useful for working over positive characteristic fields and for arithmetic problems.
There will be presented the motivations for étale and ℓ-adic cohomology, the main ideas of the constructions, and a nice example of a relatively recent application to arithmetic geometry by Esnault. The last concerns the existence of solutions for homogeneous polynomials over finite fields.
There will be presented the motivations for étale and ℓ-adic cohomology, the main ideas of the constructions, and a nice example of a relatively recent application to arithmetic geometry by Esnault. The last concerns the existence of solutions for homogeneous polynomials over finite fields.
I will try to make the imprint of the talk more popularizing than rigorous.
Séminaire des jeunes : Davide Ricci (LMV) : Some ideas on étale and ℓ-adic cohomology