Explicit calculation of Frobenius isomorphisms and Poincar\'{e} duality in the theory of arithmetic $\mathscr{D}$-modules

Tomoyuki Abe

Explicit calculation of Frobenius isomorphisms and Poincar\'{e} duality in the theory of arithmetic $\mathscr{D}$-modules

Algebraic Geometry 2011-05-31 v1

Authors: Tomoyuki Abe

Abstract

The aim of this paper is to compute the Frobenius structures of some cohomological operators of arithmetic $\ms{D}$ -modules. To do this, we calculate explicitly an isomorphism between canonical sheaves defined abstractly. Using this calculation, we establish the relative Poincar\'{e} duality in the style of SGA4. As another application, we compare the push-forward as arithmetic $\ms{D}$ -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.

Keywords

arithmetic D-modules Frobenius isomorphisms Poincaré duality rigid cohomology p-adic epsilon factors

Cite

@article{arxiv.1105.5796,
  title  = {Explicit calculation of Frobenius isomorphisms and Poincar\'{e} duality in the theory of arithmetic $\mathscr{D}$-modules},
  author = {Tomoyuki Abe},
  journal= {arXiv preprint arXiv:1105.5796},
  year   = {2011}
}

Explicit calculation of Frobenius isomorphisms and Poincar\'{e} duality in the theory of arithmetic $\mathscr{D}$-modules

Abstract

Keywords

Cite

Related papers