Grothendieck group of vector bundles
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
K_0(X)
|
| gptkbp:application |
gptkb:Riemann-Roch_theorem
index theory classification of vector bundles used in the definition of algebraic K-theory |
| gptkbp:built |
Constructed from the monoid of isomorphism classes of vector bundles under direct sum.
|
| gptkbp:category |
abelian group
|
| gptkbp:defines |
The abelian group generated by isomorphism classes of vector bundles over a topological space or scheme, modulo the relation [E] + [F] = [E ⊕ F].
|
| gptkbp:field |
gptkb:algebraic_geometry
gptkb:topology gptkb:K-theory |
| gptkbp:generalizes |
gptkb:Picard_group_(for_line_bundles)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Grothendieck group of vector bundles
|
| gptkbp:namedAfter |
gptkb:Alexander_Grothendieck
|
| gptkbp:notation |
K_0(X)
|
| gptkbp:relatedTo |
gptkb:Grothendieck_group
gptkb:algebraic_K-theory vector bundle topological K-theory |
| gptkbp:bfsParent |
gptkb:Algebraic_K-theory_of_schemes
|
| gptkbp:bfsLayer |
6
|