A structured visual guide to the major mathematical areas and their relationships.
Search by code, branch, topic, subtopic, or a keyword from the descriptions.
This subtopic studies Grothendieck groups and K_0, capturing additive invariants of exact or projective structures in algebra and geometry.
19A13 studies grothendieck groups of exact and abelian categories in Grothendieck groups K0. It studies the Grothendieck group construction that turns exact or additive structure into a universal abelian-group invariant.
Grothendieck groups of exact and abelian categories (Wikipedia)
Used to compare module categories, vector bundles, and additive invariants of rings and schemes.
19A15 studies k0 of rings and schemes in Grothendieck groups K0. It studies the Grothendieck group construction that turns exact or additive structure into a universal abelian-group invariant.
K0 of rings and schemes (Wikipedia)
Used to compare module categories, vector bundles, and additive invariants of rings and schemes.
19A22 studies positive cones and dimension groups in Grothendieck groups K0. It studies the Grothendieck group construction that turns exact or additive structure into a universal abelian-group invariant.
Positive cones and dimension groups (Wikipedia)
Used to compare module categories, vector bundles, and additive invariants of rings and schemes.
19A31 studies k0 with additional structure and operations in Grothendieck groups K0. It studies the Grothendieck group construction that turns exact or additive structure into a universal abelian-group invariant.
K0 with additional structure and operations (Wikipedia)
Used to compare module categories, vector bundles, and additive invariants of rings and schemes.
19A49 studies applications of grothendieck groups in Grothendieck groups K0. It studies the Grothendieck group construction that turns exact or additive structure into a universal abelian-group invariant.
Applications of Grothendieck groups (Wikipedia)
Used to compare module categories, vector bundles, and additive invariants of rings and schemes.