Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic D-modules

الأصل · EN

The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic D-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 D-modules and the rigid cohomologies taking Frobenius into account. These theorems will lead us to an analog of "Weil II" and a product formula for p-adic epsilon factors.