7 papers
Geometric Invariant Theory for Affine Superschemes
Alexander Quintero Velez, Pedro Rizzo, Alexander Torres-Gomez
We develop Geometric Invariant Theory for affine superschemes under the action of reductive algebraic supergroups, formulating the theory in terms of coordinate Hopf superalgebras…
The Structure of -Superschemes
Cristian Danilo Olarte, Pedro Rizzo, Alexander Torres-Gomez
This paper establishes a structural generalization of Batchelor's theorem within the framework of -superschemes. Our main result proves that any Batchelor space satisfies…
-superrings and -superschemes
Cristian Danilo Olarte, Pedro Rizzo, Alexander Torres-Gomez
This paper develops a theory of -superrings and their associated -superschemes. We prove a key equivalence between the category of fair affine -supers…
Valuations on Superrings
Pedro Rizzo, Joel Torres del Valle, Alexander Torres-Gomez
A valuation theory for superrings is developed, extending classical constructions from commutative algebra to the -graded and supercommutative setting. We define valua…
A Note on Unique Factorization in Superrings
Pedro Rizzo, Joel Torres del Valle, Alexander Torres-Gomez
In the realm of supercommutative superrings, this article investigates the unique factorization of elements. We build upon recent findings by Naser et. al. concerning similar resul…
Dedekind Superrings and Related Concepts
Pedro Rizzo, Joel Torres Del Valle, Alexander Torres-Gomez
This article investigates the properties of Dedekind superrings, invertible supermodules and projective supermodules within the -graded framework. Rather than treatin…
A note on deformations of finite dimensional modules over -algebras
Jose A. Vélez-Marulanda, Pedro Rizzo
Let be a field, and let be a (not necessarily finite dimensional) -algebra. Let be a left -module such that is finite dimensional over $\mathbb{…