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- Algebraic_K-theory abstract "In mathematics, algebraic K-theory is an important part of homological algebra concerned with defining and applying a sequenceKn(R)of functors from rings to abelian groups, for all nonnegative integers n. For historical reasons, the lower K-groups K0 and K1 are thought of in somewhat different terms from the higher algebraic K-groups Kn for n ≥ 2. Indeed, the lower groups are more accessible, and have more applications, than the higher groups. The theory of the higher K-groups is noticeably deeper, and certainly much harder to compute (even when R is the ring of integers). The group K0(R) generalises the construction of the ideal class group of a ring, using projective modules. Its development in the 1960s and 1970s was linked to attempts to solve a conjecture of Serre on projective modules that now is the Quillen–Suslin theorem; numerous other connections with classical algebraic problems were found in this era. Similarly, K1(R) is a modification of the group of units in a ring, using elementary matrix theory. The group K1(R) is important in topology, especially when R is a group ring, because its quotient the Whitehead group contains the Whitehead torsion used to study problems in simple homotopy theory and surgery theory; the group K0(R) also contains other invariants such as the finiteness invariant. Since the 1980s, algebraic K-theory has increasingly had applications to algebraic geometry. For example, motivic cohomology is closely related to algebraic K-theory.".
- Algebraic_K-theory wikiPageExternalLink books?id=TtMkTEZbYoYC.
- Algebraic_K-theory wikiPageExternalLink KThy_errata2.pdf.
- Algebraic_K-theory wikiPageExternalLink Kbook.html.
- Algebraic_K-theory wikiPageExternalLink K-theory.
- Algebraic_K-theory wikiPageExternalLink KZsurvey.pdf.
- Algebraic_K-theory wikiPageExternalLink 978-3-540-23019-9.
- Algebraic_K-theory wikiPageID "598500".
- Algebraic_K-theory wikiPageRevisionID "601682762".
- Algebraic_K-theory authorlink "Daniel Quillen".
- Algebraic_K-theory b "n".
- Algebraic_K-theory hasPhotoCollection Algebraic_K-theory.
- Algebraic_K-theory last "Quillen".
- Algebraic_K-theory p "M".
- Algebraic_K-theory year "1973".
- Algebraic_K-theory year "1974".
- Algebraic_K-theory subject Category:Algebraic_K-theory.
- Algebraic_K-theory subject Category:Algebraic_geometry.
- Algebraic_K-theory comment "In mathematics, algebraic K-theory is an important part of homological algebra concerned with defining and applying a sequenceKn(R)of functors from rings to abelian groups, for all nonnegative integers n. For historical reasons, the lower K-groups K0 and K1 are thought of in somewhat different terms from the higher algebraic K-groups Kn for n ≥ 2. Indeed, the lower groups are more accessible, and have more applications, than the higher groups.".
- Algebraic_K-theory label "Algebraic K-theory".
- Algebraic_K-theory label "Algebraïsche K-theorie".
- Algebraic_K-theory label "K-teoria algébrica".
- Algebraic_K-theory label "K-théorie algébrique".
- Algebraic_K-theory sameAs K-théorie_algébrique.
- Algebraic_K-theory sameAs 대수적_K이론.
- Algebraic_K-theory sameAs Algebraïsche_K-theorie.
- Algebraic_K-theory sameAs K-teoria_algébrica.
- Algebraic_K-theory sameAs m.02v012.
- Algebraic_K-theory sameAs Q2553675.
- Algebraic_K-theory sameAs Q2553675.
- Algebraic_K-theory wasDerivedFrom Algebraic_K-theory?oldid=601682762.
- Algebraic_K-theory isPrimaryTopicOf Algebraic_K-theory.