Normal hyperplane sections of normal schemes in mixed characteristic

Abstract

The aim of this article is to prove that, under certain conditions, an affine flat normal scheme that is of finite type over a local Dedekind scheme in mixed characteristic admits infinitely many normal effective Cartier divisors. For the proof of this result, we prove the Bertini theorem for normal schemes of some type. We apply the main result to prove a result on the restriction map of divisor class groups of Grothendieck–Lefschetz type in mixed characteristic.