On Weil Polynomials of K3 Surfaces

Abstract. For K3 surfaces, we derive some conditions the characteristic polynomial of the Frobenius on the ´etale cohomology must satisfy. These conditions may be used to speed up the computation of Picard numbers and the decision of the sign in the functional equation∗∗ . Our investigations are based on the Artin-Tate formula.

• Type: Conference
• Year: 2010
• Where: ANTS
• Authors: Andreas-Stephan Elsenhans, Jörg Jahnel
• Keywords: Algorithms, ANTS 2010, Characteristic Polynomial, Picard Numbers, ´etale Cohomology