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We study Frobenius eigenvalues of the compactly supported rigid cohomology ofa variety defined over a finite field of $q$ elements via Dwork's method. Acouple of arithmetic consequences will be drawn from this study. As the firstapplication, we show that the zeta functions for finitely many related affinevarieties are capable of witnessing all Frobenius eigenvalues of the rigidcohomology of the variety up to Tate twist. This result does not seem to beknown for $\ell$-adic cohomology. As the second application, we prove several$q$-divisibility lower bounds for Frobenius eigenvalues of the rigid cohomologyof the variety in terms of the multi-degrees of the defining equations. Thesedivisibility bounds for rigid cohomology are generally better than what issuggested from the best known divisibility bounds in $\ell$-adic cohomology,both before and after the middle cohomological dimension.

Revisiting Dwork cohomology: Visibility and divisibility of Frobenius eigenvalues in rigid cohomology