Metraipolis › archive › dc_facef604b86e

Algebraic cobordism — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Algebraic_cobordism
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-08T10:29:10.260Z
SHA-256 of the archived text: 4306cec80adca720b884bf6df9464e4b087e61b8181602c0dfd3080bb2a881a9
Stable URL of this page: https://metraipolis.com/documento/dc_facef604b86e

How to cite

Algebraic cobordism — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Algebraic_cobordism (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_facef604b86e (Metraipolis archive dc_facef604b86e, sha256 4306cec80adca720b884bf6df9464e4b087e61b8181602c0dfd3080bb2a881a9)

BibTeX

@misc{dcfacef604b86e,
  title = {Algebraic cobordism — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Algebraic_cobordism},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_facef604b86e; sha256 4306cec80adca720b884bf6df9464e4b087e61b8181602c0dfd3080bb2a881a9},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Algebraic_cobordism. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, algebraic cobordism is an analogue of complex cobordism for smooth quasi-projective schemes over a field. It was introduced by Marc Levine and Fabien Morel (2001, 2001b). An oriented cohomology theory on the category of smooth quasi-projective schemes Sm over a field k consists of a contravariant functor A* from Sm to commutative graded rings, together with push-forward maps f* whenever f:Y→X has relative dimension d for some d. These maps have to satisfy various conditions similar to those satisfied by complex cobordism. In particular they are "oriented", which means roughly that they behave well on vector bundles; this is closely related to the condition that a generalized cohomology theory has a complex orientation. Over a field of characteristic 0, algebraic cobordism is the universal oriented cohomology theory for smooth varieties. In other words there is a unique morphism of oriented cohomology theories from algebraic cobordism to any other oriented cohomology theory. Levine (2002) and Levine & Morel (2007) give surveys of algebraic cobordism. The algebraic cobordism ring of generalized flag varieties has been computed by Hornbostel & Kiritchenko (2011).

Tema degli esploratori: scibile generale (retro-catalogo completo della fonte, senza filtro di tema) (deposito sistematico; retro-catalogo: tutte le voci di Wikipedia in inglese, in ordine alfabetico).
Fonte: Wikipedia in inglese, voce «Algebraic cobordism» — https://en.wikipedia.org/wiki/Algebraic_cobordism
Wikidata Q4723991 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4723991
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Algebraic_cobordism?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1189684059, consultata il 2026-11-08T10:24:46.201Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: a2b3fa2a18eda4850720b421c688126e471a6f16046a59b0b6a6be942f6e409a