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Mathematics > Algebraic Geometry

arXiv:1807.10812 (math)
[Submitted on 27 Jul 2018 (v1), last revised 26 Jan 2019 (this version, v2)]

Title:Weil Conjectures Exposition

Authors:Evgeny Goncharov
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Abstract:In this paper we provide a full account of the Weil conjectures including Deligne's proof of the conjecture about the eigenvalues of the Frobenius endomorphism.
Section 1 is an introduction into the subject. Our exposition heavily relies on the Etale Cohomology theory of Grothendieck so I included an overview in Section 2. Once one verifies (or takes for granted) the results therein, proofs of most of the Weil conjectures are straightforward as we show in Section 3.
Sections 4-8 constitute the proof of the remaining conjecture. The exposition is mostly similar to that of Deligne in [7] though I tried to provide more details whenever necessary. Following Deligne, I included an overview of Lefschetz theory (that is crucial for the proof) in Section 6.
Section 9 contains a (somewhat random and far from complete) account of the consequences. Numerous references are mentioned throughout the paper as well as briefly discussed in Subsection 1.4.
Comments: 49 pages
Subjects: Algebraic Geometry (math.AG)
Cite as: arXiv:1807.10812 [math.AG]
  (or arXiv:1807.10812v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1807.10812

Submission history

From: Evgeny Goncharov [view email]
[v1] Fri, 27 Jul 2018 19:48:28 UTC (43 KB)
[v2] Sat, 26 Jan 2019 05:12:29 UTC (43 KB)
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