The Relation Type of Varieties
Maryam Akhavin, Abbas Nasrollah Nejad

TL;DR
This paper introduces the relation type of analytic and formal algebras, demonstrating its invariance and defining it via Andre9-Quillen homology, with applications to schemes, varieties, and algebroid structures.
Contribution
It defines the relation type for various algebraic structures and proves its invariance using homological methods, extending understanding of algebraic and geometric invariants.
Findings
Relation type is well-defined and invariant.
Relation type can be described using Andre9-Quillen homology.
Invariant for schemes, varieties, and algebroid varieties.
Abstract
In this paper, we introduce the notion of relation type of analytic and formal algebras and prove that it is well-defined and invariant by describing this notion in terms of the Andr\'e-Quillen homology and using the Jacobi-Zariski long exact sequence of homology. In particular, the relation type is an invariant of schemes of finite type over a field, analytic varieties, and algebroid varieties.
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.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Alkaloids: synthesis and pharmacology · Algebraic structures and combinatorial models
