Weil conjectures

In mathematics, the Weil conjectures were some highly influential proposals by André Weil on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields. Quotes There can be no doubt that proving the Weil conjectures was the ultimate goal that Grothendieck had in mind with his reconstruction of algebraic geometry. Chapter 10. The Weil Conjectures https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Spirituality/Spirituality10.pdf Like Moses, André Weil caught sight of the Promised Land, but unlike Moses, he was unable to cross the Red Sea on dry land, nor did he have an adequate vessel. Pierre Cartier (mathematician) Cartier Pierre 2004 Un pays dont on ne connaîtrait que le nom (Grothendieck et les " motifs ") http://www.math.jussieu.fr/~leila/grothendieckcircle/cartier.pdf French Réel en mathématiques-psychanalyse et mathématiques Cartier Pierre Charraud Nathalie Editions Agalma , English translation: A country of which nothing is known but the name Grothendieck and "motives". Just as Weil's conjectures were about counting solutions to equations in a situation where the number of solutions is known to be finite, the BSD conjecture concerns the simplest class of polynomial equations—elliptic curves—for which there is no simple way to decide whether the number of solutions is finite or infinite. Michael Harris Mathematics without Apologies: Portrait of a Problematic Vocation https://books.google.com/books?id=zfmhDQAAQBAJ&pg=PA27 30 May 2017 Princeton University Press 978-1-4008-8552-7 27 External links Category:Mathematical theorems