Families of algebraic varieties parametrized by topological spaces
J. H. Teh

TL;DR
This paper explores families of algebraic varieties parametrized by topological spaces, extending classical algebraic geometry results and establishing an equivalence between certain sheaf categories.
Contribution
It generalizes classical results like Hilbert Nullstellensatz and primary decomposition to parametrized families and proves an equivalence between bivariant coherent sheaves and sheaves of finitely generated modules.
Findings
Generalization of Hilbert Nullstellensatz to parametrized families
Extension of primary decomposition results
Equivalence between bivariant coherent sheaves and finitely generated module sheaves
Abstract
We study families of algebraic varieties parametrized by topological spaces and generalize some classical results such as Hilbert Nullstellensatz and primary decomposition of commutative rings. We show that there is an equivalence between the category of bivariant coherent sheaves and the category of sheaves of finitely generated modules.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic structures and combinatorial models · Rings, Modules, and Algebras
