A $p$-Adic Theory of Hyperfunctions, I

Abstract

Publisher Summary This chapter presents a p-adic theory of hyperfunctions of several variables by using relative cohomologies of rigid analytic spaces. The chapter reviews the general theory of relative cohomologies of rigid analytic spaces, and discusses the relation between the usual topology of K and the Grothendieck topology of X. A lemma on the relative cohomologies on a polydisk is proven, and the duality is obtained. As for the theory of rigid analytic spaces, the terminology of Bosch-Gunter-Remmert is used. Projective limits, and various lemmas are presented in the chapter. The chapter also proves various theorems.