The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic -modules. To do this, we calculate explicitly an isomorphism between canonical sheaves defined abstractly. Using this calculation, we establish the relative Poincaré duality in the style of SGA4. As another application, we compare the push-forward as arithmetic -modules and the rigid cohomologies taking Frobenius into account. These theorems will be used to prove "-adic Weil II" and a product formula for -adic epsilon factors.
Cite this article
Tomoyuki Abe, Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic -modules. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 89–149DOI 10.4171/RSMUP/131-7