ANALYTIC SPECTRUM OF RIG CATEGORIES

Abstract

Abstract. We define the analytic spectrum of a rig category (A, ⊕, ⊗), and equip it with a sheaf of categories of rational functions. If the category is additive, we define a sheaf of categories of analytic functions. We relate this construction to Berkovich’s analytic spaces, to Durov’s generalized schemes and to Haran’s F-schemes. We use these relations to define analytic versions of Arakelov compactifications of affine arithmetic varieties. 1