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.
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