Grothendieck ring of schemes
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:King
gptkb:mathematical_concept |
| gptkbp:alsoKnownAs |
gptkb:Grothendieck_ring_of_varieties
|
| gptkbp:builtBy |
isomorphism classes of schemes
|
| gptkbp:category |
schemes of finite type over a field k
|
| gptkbp:citation |
F. Loeser, J. Denef, "Motivic integration and the Grothendieck group of pseudo-finite fields"
J. Kollár, "Grothendieck ring of varieties and motivic integration" |
| gptkbp:containsElement |
class of the affine line (Lefschetz motive)
|
| gptkbp:field |
gptkb:algebraic_geometry
|
| gptkbp:generalizes |
Grothendieck group of varieties
|
| https://www.w3.org/2000/01/rdf-schema#label |
Grothendieck ring of schemes
|
| gptkbp:loveInterest |
[X] = [Y] + [X \\ Y] for closed subscheme Y of X
|
| gptkbp:namedAfter |
gptkb:Alexander_Grothendieck
|
| gptkbp:notation |
K_0(Sch/k)
|
| gptkbp:operator |
addition by disjoint union
multiplication by product of schemes |
| gptkbp:relatedTo |
gptkb:motivic_zeta_function
motivic measure |
| gptkbp:usedIn |
gptkb:motivic_integration
enumerative geometry |
| gptkbp:bfsParent |
gptkb:Grothendieck_ring
|
| gptkbp:bfsLayer |
7
|