Nontrivial vector bundles with trivial Chern classes
Satya Mandal

TL;DR
This paper constructs specific smooth affine algebras and projective modules over them with trivial total Chern class but nontrivial K-theory class, revealing subtle properties of vector bundles.
Contribution
It introduces new examples of vector bundles with trivial Chern classes that are nonetheless nontrivial in K-theory, expanding understanding of vector bundle classification.
Findings
Existence of smooth affine algebras with dimension p+2 for prime p
Construction of projective modules with trivial total Chern class
Identification of nontrivial K-theory classes despite trivial Chern classes
Abstract
Let be an algebraically closed field, with . In this article, for prime numbers , we construct smooth affine algebras over , with . Further, we construct projective -modules with , such that in and the total Chern class is trivial. We use the splitting theorem in \cite{ABH} that for projective -modules with , vanishing .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Operator Algebra Research · Geometry and complex manifolds
