Picard Groups and Class Groups of Monoid Schemes

Published 20 Jun 2013 in math.AG | (1306.4928v2)

Abstract: We define and study the Picard group of a monoid scheme and the class group of a normal monoid scheme. To do so, we develop some ideal theory for (pointed abelian) noetherian monoids, including primary decomposition and discrete valuations. The normalization of a monoid turns out to be a monoid scheme, but not always a monoid.

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