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Analytic spectrum of rig categories

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Frederic Paugam

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.

Keywords:
Rig categories, global analytic geometry, generalized rings,
Arakelov compactifications

2010 MSC:
18D10, 14G22, 14G25, 11G35, 18C15

*Theory and Applications of Categories,*
Vol. 29, 2014,
No. 6, pp 188-197.

Published 2014-04-21.

http://www.tac.mta.ca/tac/volumes/29/6/29-06.pdf

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