The Quillen–Suslin theorem, also known as Serre's problem or Serre's conjecture, is a theorem in commutative algebra concerning the relationship between...

or a (multivariate) polynomial ring over a field (this is the Quillen–Suslin theorem). Projective modules were first introduced in 1956 in the influential...

mathematics, Suslin's theorem may refer to: The Quillen–Suslin theorem (formerly the Serre conjecture), due to Andrei Suslin. Any of several theorems about analytic...

Serre's conjecture may refer to: Quillen–Suslin theorem, formerly known as Serre's conjecture Serre's conjecture II, concerning the Galois cohomology of...

Daniel Gray Quillen (June 22, 1940 – April 30, 2011) was an American mathematician. He is known for being the "prime architect" of higher algebraic K-theory...

Alexander Suslin (died 1349), German Orthodox rabbi and Talmudist Andrei Suslin (1950–2018), Russian mathematician known for Suslin homology Quillen–Suslin theorem...

of the Quillen–Suslin theorem, a result in commutative algebra, first conjectured by Jean-Pierre Serre in 1955, and then proved by Daniel Quillen and Andrei...

Complete intersection ring Koszul complex Hilbert's syzygy theorem Quillen–Suslin theorem Height (ring theory) Depth (ring theory) Hilbert polynomial...

dimension. This result may be proven using Serre's theorem on regular local rings. Quillen–Suslin theorem Hilbert series and Hilbert polynomial D. Hilbert...

Puiseux's theorem (algebraic geometry) Pythagorean theorem (geometry) Quillen–Suslin theorem (abstract algebra) Quadratic reciprocity theorem Quantum threshold...

Jean-Pierre Serre, a French mathematician. Bass–Serre theory Serre class Quillen–Suslin theorem (sometimes known as "Serre's Conjecture" or "Serre's problem") Serre's...

as of September 2022[update]. The conjecture terminology may persist: theorems often enough may still be referred to as conjectures, using the anachronistic...

color theorem is proved by Kenneth Appel and Wolfgang Haken, the first major theorem to be proved using a computer. Andrei Suslin and Daniel Quillen independently...

Karoubi–Villamayor 1971 Milnor 1970 Milnor 1970, p. 319 Nesterenko–Suslin 1990 Totaro 1992 Thomason 1992 Quillen 1971 Segal 1974 Wall 1965 Siebenmann 1965 Smale 1962...

raised by Jean-Pierre Serre and was later proved by Quillen and Suslin; see Quillen–Suslin theorem. More generally, the conjecture was shown by Lindel...

to an analogy between projective modules and vector bundles. The Quillen–Suslin theorem asserts that any finitely generated projective module over k[T1...

Free object Projective object free presentation free resolution Quillen–Suslin theorem stably free module generic freeness Keown (1975). An Introduction...

Homological types: Projective module Projective cover Swan's theorem Quillen–Suslin theorem Injective module Injective hull Flat module Flat cover Coherent...

In particular, every line bundle is trivial. More generally, the Quillen–Suslin theorem implies that every algebraic vector bundle over an affine space...

& Suslin 1982) harv error: no target: CITEREFMerkurjevSuslin1982 (help) and is known as the Merkurjev–Suslin theorem. Later, Merkurjev and Suslin, and...

Vaseršteĭn (born 1944), mathematician known for providing a proof of Quillen–Suslin theorem Lev Vekker (1918–2001), psychologist Vladimir Voevodsky (1966–2017)...

projective module. pure submodule pure submodule Quillen–Suslin theorem The Quillen–Suslin theorem states that a finite projective module over a polynomial...

proved the Merkurjev–Suslin theorem on the norm residue homomorphism in Milnor K2-theory, with applications to the Brauer group. Suslin was an invited speaker...

affirmative by Daniel Quillen and Andrei Suslin independently in 1976. This result is now known as the Quillen–Suslin theorem. Serre, at twenty-seven...

2014, with a diploma thesis in pure mathematics related to the Quillen–Suslin theorem. She continued her studies at the University of Potsdam in the Potsdam...

even}}\end{cases}}} For n=2, this can be seen from Matsumoto's theorem, in higher degrees it was computed by Quillen in conjunction with his work on the Adams conjecture...

stable range. The concept of homological stability was pioneered by Daniel Quillen whose proof technique has been adapted in various situations. Examples...

invertible in A vanishes. Jardine (1993) used Gabber's result and Suslin rigidity to reprove Quillen's computation of the K-theory of finite fields. Noncommutative...

are related by the universal coefficient theorem, as in topology. By Bloch, Lichtenbaum, Friedlander, Suslin, and Levine, there is a spectral sequence...

Bloch group is a cohomology group of the Bloch–Suslin complex, named after Spencer Bloch and Andrei Suslin. It is closely related to polylogarithm, hyperbolic...