Related papers: Picard Groups and Class Groups of Monoid Schemes

We characterize the category of monads on $Set$ and the category of Lawvere theories that are equivalent to the category of regular equational theories.

We define a general notion of centrally $\Gamma$-graded sets and groups and of their graded products, and prove some basic results about the corresponding categories: most importantly, they form braided monoidal categories. Here, $\Gamma$…

We construct a singular homology theory on the category of schemes of finite type over a Dedekind domain and verify several basic properties. For arithmetic schemes we construct a reciprocity isomorphism between the integral singular…

This paper studies the K-theory of categories of partially cancellative monoid sets, which is better behaved than that of all finitely generated monoid sets. A number of foundational results are proved, making use of the formalism of…

We investigate the notion of soficity for monoids. A group is sofic as a group if and only if it is sofic as a monoid. All finite monoids, all commutative monoids, all free monoids, all cancellative one-sided amenable monoids, all…

The aim of this paper is to solve a problem proposed by Dominique Bourn: to provide a categorical-algebraic characterisation of groups amongst monoids and of rings amongst semirings. In the case of monoids, our solution is given by the…

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K_0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify…

An automorphism of a group is said to be normal if it preserves each normal subgroup. In this paper, we determine the normal automorphisms of a free metabelian nilpotent group.

In this paper we introduce toric rings of multicomplexes. We show how to compute the divisor class group and the class of the canonical module when the toric ring is normal. In the special case that the multicomplex is a discrete…

We introduce logarithmic Picard algebroids, a natural class of Lie algebroids adapted to a simple normal crossings divisor on a smooth projective variety. We show that such algebroids are classified by a subspace of the de Rham cohomology…

We describe quantizations on monoidal categories of modules over finite groups. They are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over S3 and A4 we are given…

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…

We build a concrete and natural model for the strict 2-category of orbifolds. In particular we prove that if one localizes the 2-category of proper etale Lie groupoids at a class of 1-arrows that we call "covers", then the strict 2-category…

We compute the Picard group of the moduli stack of stable hyperelliptic curves of any genus, exhibiting explicit and geometrically meaningful generators and relations.

In this paper, we extend the classical theory of crossed $G$-sets and the crossed Burnside ring from a finite group $G$ to a finite groupoid $\mathcal{G}$. We introduce a natural monoidal structure on the category of crossed…

In this paper we continue Prasma's homotopical group theory program by considering homotopy normal maps in arbitrary $\infty$-topoi. We show that maps of group objects equipped with normality data, in Prasma's sense, are algebras for a…

A smooth cuboid can be identified with a $3\times 3$ matrix of linear forms, with coefficients in a field $K$, whose determinant describes a smooth cubic in the projective plane. To each such matrix one can associate a group scheme over…

We propose an explicit formula for the Segre classes of monomial subschemes of nonsingular varieties, such as schemes defined by monomial ideals in projective space. The Segre class is expressed as a formal integral on a region bounded by…

A group is called metahamiltonian if all non-abelian subgroups of it are normal. This concept is a natural generation of Hamiltonian groups. In this paper, a complete classification of finite metahamiltonian $p$-groups is given.

We introduce a theory for encoding and manipulating algebraic data on categories via $\textit{concentration structures}$, which are equivalence relations on morphisms that satisfy certain axioms. For any category with a concentration…