Divisibility of Frobenius eigenvalues

The information of Hasse-Weil zeta function of an algebraic variety over a finite field can be captured by the l-adic or rigid cohomology.  Thus the p-divisibility of Frobenius eigenvalues controls the p-adic location of reciprocal zeros and reciprocal poles of the zeta function.  I shall explain some divisibility bounds of these Frobenius eigenvalues, in terms of the shape of defining equations, improving known bounds of Esnault-Katz.  I shall also discuss Hodge-theoretic analogues of these bounds.  This talk is based on a joint work with Daqing Wan.

学术海报.pdf