Grothendieck ring of varieties
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
K_0(Var_k)
|
| gptkbp:application |
gptkb:motivic_integration
motivic measures study of birational geometry |
| gptkbp:citation |
F. Loeser, J. Denef, "Motivic integration, quotient singularities and the McKay correspondence"
Larsen, Lunts, "Motivic measures and stable birational geometry" |
| gptkbp:contains |
gptkb:Lefschetz_motive
|
| gptkbp:containsElement |
[X], where X is a variety over k
|
| gptkbp:defines |
the free abelian group generated by isomorphism classes of algebraic varieties over a field k, modulo the relation [X] = [Y] + [X \\ Y] for closed subvarieties Y of X
|
| gptkbp:field |
gptkb:algebraic_geometry
|
| https://www.w3.org/2000/01/rdf-schema#label |
Grothendieck ring of varieties
|
| gptkbp:loveInterest |
[X] = [Y] + [X \\ Y] for closed subvariety Y of X
|
| gptkbp:namedAfter |
gptkb:Alexander_Grothendieck
|
| gptkbp:notation |
K_0(Var_k)
|
| gptkbp:operator |
multiplication given by product of varieties
|
| gptkbp:relatedTo |
gptkb:algebraic_K-theory
gptkb:motivic_integration gptkb:motivic_zeta_function motivic measure |
| gptkbp:structure |
commutative ring
|
| gptkbp:unitElement |
class of the point variety
|
| gptkbp:bfsParent |
gptkb:Grothendieck_ring
gptkb:motivic_Milnor_fiber |
| gptkbp:bfsLayer |
7
|