JournalsrsmupVol. 131pp. 89–149

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

  • Tomoyuki Abe

    The University of Tokyo, Kashiwa, Chiba, Japan
Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic $\mathcal D$-modules cover
Download PDF

Abstract

The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic D{\mathcal 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{\mathcal D}-modules and the rigid cohomologies taking Frobenius into account. These theorems will be used to prove "pp-adic Weil II" and a product formula for pp-adic epsilon factors.

Cite this article

Tomoyuki Abe, Explicit calculation of Frobenius isomorphisms and Poincaré duality in the theory of arithmetic D\mathcal D-modules. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 89–149

DOI 10.4171/RSMUP/131-7