منابع مشابه
The Weil Conjectures
The Weil conjectures constitute one of the central landmarks of 20th century algebraic geometry: not only was their proof a dramatic triumph, but they served as a driving force behind a striking number of fundamental advances in the field. The conjectures treat a very elementary problem: how to count the number of solutions to systems of polynomial equations over finite fields. While one might ...
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We give a proof that the Riemann hypothesis for hypersurfaces over finite fields implies the result for all smooth proper varieties, by a deformation argument which does not use the theory of Lefschetz pencils or the `-adic Fourier transform.
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Let κ = Fq be a finite field of characteristic p > 0, and k be a fixed algebraic closure of κ. We fix a prime ` 6= p, and an isomorphism τ : Q` → C. Whenever we want to denote something (e.g. scheme, sheaf, morphism, etc.) defined over κ, we will put a subscript 0 (e.g. X0 is a scheme over κ, F0 is a Weil sheaf defined over X0, etc.), and when the subscript is dropped, this means the correspond...
متن کاملDescent Identities, Hessenberg Varieties, and the Weil Conjectures
We apply the Weil conjectures to the Hessenberg Varieties to obtain information about the combinatorics of descents in the symmetric group. Combining this with elementary linear algebra leads to elegant proofs of some identities from the theory of descents. 3
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The story of the Weil conjectures and the development of etale cohomology is the story of one of the great triumphs of 20th century algebraic geometry. The problem treated is exceedingly elementary – counting solutions of polynomials over finite fields – but the proofs require and indeed motivated the creation of an astonishing array of sophisticated technical machinery. The earliest echoes of ...
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ژورنال
عنوان ژورنال: Notices of the American Mathematical Society
سال: 2021
ISSN: 0002-9920,1088-9477
DOI: 10.1090/noti2211