The earliest antecedent of the Weil conjectures is by Carl Friedrich Gauss and appears in section VII of his Disquisitiones Arithmeticae (Mazur 1974), concerned with See more

Weil suggested that the conjectures would follow from the existence of a suitable "Weil cohomology theory" for varieties over finite fields, similar to the usual cohomology with … See more

Verdier (1974), Serre (1975), Katz (1976) and Freitag & Kiehl (1988) gave expository accounts of the first proof of Deligne (1974). Much of the … See more

Suppose that X is a non-singular n-dimensional projective algebraic variety over the field Fq with q elements. The zeta function ζ(X, s) of X … See more

The projective line
The simplest example (other than a point) is to take X to be the projective line. The number of points of X over a field with q elements is just Nm … See more

By the end of 1964 Grothendieck together with Artin and Jean-Louis Verdier (and the earlier 1960 work by Dwork) proved the Weil conjectures … See more

Deligne (1980) found and proved a generalization of the Weil conjectures, bounding the weights of the pushforward of a sheaf. In … See more