Weil Conjectures I (translation of La Conjecture de Weil I by Pierre Deligne)

TL;DR

This paper provides a comprehensive translation of Pierre Deligne's proof of the first Weil conjecture, making the complex mathematical arguments accessible to a broader audience.

Contribution

It offers the first complete translation of Deligne's proof of Weil Conjectures I, along with detailed explanations and contextual notes for better understanding.

Findings

Proof of Weil Conjectures I fully translated and explained

Clarifications and detailed overview provided for complex proofs

Accessible resource for understanding Deligne's groundbreaking work

Abstract

I attempted to write the full translation of this article to make the remarkable proof of Pierre Deligne available to a greater number of people. Overviews of the proofs can be found elsewhere. I especially recommend the notes of James Milne on Etale Cohomology that also contain a justification for the theory underlying this article and proofs of the results used by Deligne. The footnotes are mostly claims that some details appear in Milne, clarifications of some of the terminology or my personal struggles. I have also made a thorough overview of the proof together with more detailed explanations - arXiv:1807.10812. Enjoy!