Eigenvalues of Frobenius acting on the ℓ-adic cohomology of complete intersections of low degree

✍ Scribed by Hélène Esnault

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 91 KB
• Volume: 337
• Category: Article
• ISSN: 1631-073X
• DOI: 10.1016/s1631-073x(03)00370-4

✦ Synopsis

We show that the eigenvalues of Frobenius acting on -adic cohomology of a complete intersection of low degree defined over the finite field F q modulo the cohomology of the projective space are divisible as algebraic integers by q κ , where the natural number κ is predicted by the theorem of Ax and Katz (Amer J. Math. 93 (1971) 485-499) on the congruence for the number of rational points.