Dwork hypersurfaces of degree six and Greene’s hypergeometric function

The number of Fp-points on Dwork hypersurfaces and hypergeometric functions

Dwork cohomology, de Rham cohomology, and hypergeometric functions

In the 1960’s, Dwork developed a p-adic cohomology theory of de Rham type for varieties over finite fields, based on a trace formula for the action of a Frobenius operator on certain spaces of p-analytic functions. One can consider a purely algebraic analogue of Dwork’s theory for varieties over a field of characteristic zero and ask what is the connection between this theory and ordinary de Rh...

An Explicit Factorisation of the Zeta Functions of Dwork Hypersurfaces

Let Fq be a finite field with q elements, ψ a non-zero element of Fq, and n an integer ≥ 3 prime to q. The aim of this article is to show that the zeta function of the projective variety over Fq defined by Xψ : x n 1 + · · · + x n n − nψx1 . . . xn = 0 has, when n is prime and Xψ is non singular (i.e. when ψ 6= 1), an explicit decomposition in factors coming from affine varieties of odd dimensi...

Isotypic decomposition of the cohomology and factorization of the zeta functions of Dwork hypersurfaces

The aim of this article is to illustrate, on the Dwork hypersurfaces xn1+· · ·+x n n−nψx1 . . . xn = 0 (with n an integer ≥ 3 and ψ ∈ F∗ q a parameter satisfying ψ n 6= 1), how the study of the representation of a finite group of automorphisms of a hypersurface in its etale cohomology allows to factor its zeta function.

Families of hypersurfaces of large degree

We show that general moving enough families of high degree hypersurfaces in P do not have a dominant set of sections.