Geodesic
Analytic spectrum of rig categories
Theory and applications of categories, Tome 29 (2014), pp. 188-197 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We define the analytic spectrum of a rig category $(A,\oplus,\otimes)$, 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.

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Classification : 18D10, 14G22, 14G25, 11G35, 18C15
Keywords: Rig categories, global analytic geometry, generalized rings, Arakelov compactifications 
@article{TAC_2014_29_a5,
     author = {Frederic Paugam},
     title = {Analytic spectrum of rig categories},
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     pages = {188--197},
     year = {2014},
     volume = {29},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2014_29_a5/}
}
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Frederic Paugam. Analytic spectrum of rig categories. Theory and applications of categories, Tome 29 (2014), pp. 188-197. http://geodesic.mathdoc.fr/item/TAC_2014_29_a5/