Picard Groups and Class Groups of Monoid Schemes
Jaret Flores, Charles Weibel

TL;DR
This paper introduces the concepts of Picard and class groups for monoid schemes, developing ideal theory for noetherian monoids and exploring normalization properties.
Contribution
It defines Picard and class groups for monoid schemes and develops ideal theory, including primary decomposition and valuations, for noetherian monoids.
Findings
Normalization of a monoid can be a monoid scheme but not necessarily a monoid.
Developed ideal theory for pointed abelian noetherian monoids.
Established properties of Picard and class groups in the context of monoid schemes.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
