Hypersurfaces and the Weil conjectures
نویسنده
چکیده
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.
منابع مشابه
Navigating the motivic world
Contents Introduction 1 Chapter 1. Introduction to the Weil conjectures 3 1. A first look 3 2. Formal statement of the conjectures 8 3. Zeta functions 11 4. A plan to prove the conjectures 14 5. Some history of the proofs of the conjectures 18 A. Computer calculations 20 B. Computations for diagonal hypersurfaces 25 Chapter 2. Topological interlude: the cohomology of algebraic varieties 35 1. L...
متن کاملAn Application of the Weil Conjectures to PAC and Large Fields
This expository paper gives an elementary proof, using the Weil Conjectures for curves, that an infinite algebraic extension of a finite field is PAC and large.
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
متن کامل2 . Points over Finite Fields and the Weil Conjectures
In this chapter we will relate the topology of smooth projective varieties over the complex numbers with counting points over finite fields, via the Weil conjectures. If X is a variety defined over a finite field Fq, one can count its points over the various finite extensions of Fq; denote Nm = |X(Fmq )| (for instance, if X ⊂ AnFq is affine, given by equations f1, . . . , fk, then Nm = |{x ∈ Fm...
متن کاملWeil conjectures for abelian varieties over finite fields
This is an expository paper on zeta functions of abelian varieties over finite fields. We would like to go through how zeta function is defined, and discuss the Weil conjectures. The main purpose of this paper is to fill in more details to the proofs provided in Milne. Subject to length constrain, we will not include a detailed proof for Riemann hypothesis in this paper. We will mainly be follo...
متن کامل