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1
S Anantharaman ,
Schémas en groupes,
espaces homogènes et espaces algébriques sur une base de
dimension 1 , from: "Sur les
groupes algébriques", Mém. Soc. Math. France 33, Soc. Math.
France (1973) 5 MR0335524
2
M Artin , Versal deformations and
algebraic stacks , Invent. Math. 27 (1974) 165 MR0399094
3
M Artin , A
Grothendieck , J L Verdier ,
Théorie des topos et cohomologie étale des schémas, Tome 1
: Théorie des topos, Exposés I–IV (SGA 4 1
) , 269, Springer (1972) MR0354652
4
A Asok , B
Doran , J Fasel , Smooth models of motivic
spheres and the clutching construction , Int. Math. Res.
Not. 2017 (2017) 1890 MR3658186
5
A Asok , J
Fasel , Algebraic vector
bundles on spheres , J. Topol. 7 (2014) 894 MR3252968
6
A Asok , J
Fasel , A cohomological
classification of vector bundles on smooth affine
threefolds , Duke Math. J. 163 (2014) 2561 MR3273577
7
A Asok , J
Fasel , Splitting
vector bundles outside the stable range and 𝔸 1 –homotopy sheaves of punctured affine
spaces , J. Amer. Math. Soc. 28 (2015) 1031 MR3369908
8
A Asok , J
Fasel , Euler class groups and motivic stable
cohomotopy , preprint (2016) arXiv:1601.05723
9
A Asok , M
Hoyois , M Wendt , Affine
representability results in 𝔸 1 –homotopy theory, I : vector
bundles , Duke Math. J. 166 (2017) 1923 MR3679884
10
A Asok , M
Hoyois , M Wendt , Generically split octonion
algebras and 𝔸 1 –homotopy theory , preprint (2017)
arXiv:1704.03657
11
A Bak , Nonabelian K –theory : the nilpotent class of K 1 and
general stability , K –Theory 4 (1991) 363 MR1115826
12
A Bak , R
Hazrat , N Vavilov , Localization-completion
strikes again : relative K 1 is
nilpotent by abelian , J. Pure Appl. Algebra 213 (2009)
1075 MR2498798
13
C Balwe , A
Sawant , R –equivalence and 𝔸 1 –connectedness in anisotropic
groups , Int. Math. Res. Not. 2015 (2015) 11816 MR3456703
14
C Balwe , A
Sawant , 𝔸 1 –connectedness in reductive algebraic
groups , Trans. Amer. Math. Soc. 369 (2017) 5999
MR3646787
15
J Barge , J
Lannes , Suites de Sturm,
indice de Maslov et périodicité de Bott , 267,
Birkhäuser (2008) MR2431916
16
H Bass , E H
Connell , D L Wright , Locally polynomial
algebras are symmetric algebras , Invent. Math. 38
(1976) 279 MR0432626
17
P Belmans , A J
de Jong , others , The Stacks project ,
http://stacks.math.columbia.edu, electronic reference
(2005–)
18
A Białynicki-Birula ,
Rationally
trivial homogeneous principal fibrations of schemes ,
Invent. Math. 11 (1970) 259 MR0276250
19
A Borel , Linear algebraic
groups , 126, Springer (1991) MR1102012
20
C Cazanave ,
Algebraic
homotopy classes of rational functions , Ann. Sci. Éc.
Norm. Supér. 45 (2012) 511 MR3059240
21
J L
Colliot-Thélène , M Ojanguren , Espaces principaux
homogènes localement triviaux , Inst. Hautes Études Sci.
Publ. Math. 75 (1992) 97 MR1179077
22
B Conrad , Reductive
group schemes , from: "Autour des schémas en groupes, I",
Panor. Synthèses 42/43, Soc. Math. France (2014) 93 MR3362641
23
B Conrad , O
Gabber , G Prasad , Pseudo-reductive
groups , 17, Cambridge Univ. Press (2010) MR2723571
24
M Demazure , A
Grothendieck ,
Schémas en groupes, Tome II : Groupes de type
multiplicatif, et structure des schémas en groupes généraux,
Exposés VIII–XVIII (SGA 3 II
) , 152, Springer (1970) MR0274459
25
M Demazure , A
Grothendieck ,
Schémas en groupes, Tome III : Structure des schémas en
groupes réductifs, Exposés XIX–XXVI (SGA 3 III
) , 153, Springer (1970) MR0274460
26
D Dugger , S
Hollander , D C Isaksen , Hypercovers and
simplicial presheaves , Math. Proc. Cambridge Philos.
Soc. 136 (2004) 9 MR2034012
27
J Fasel , Some remarks on orbit sets of
unimodular rows , Comment. Math. Helv. 86 (2011) 13
MR2745274
28
J Fasel , On the number of
generators of ideals in polynomial rings , Ann. of Math.
184 (2016) 315 MR3505181
29
R Fedorov , I
Panin , A proof of the
Grothendieck–Serre conjecture on principal bundles over regular
local rings containing infinite fields , Publ. Math.
Inst. Hautes Études Sci. 122 (2015) 169 MR3415067
30
P Gille , Le
problème de Kneser–Tits , from: "Séminaire Bourbaki,
2007/2008", Astérisque 326, Soc. Mat. de France (2009) 39
MR2605318
31
P Gille , Sur la
classification des schémas en groupes semi-simples , from:
"Autour des schémas en groupes, III", Panor. Synthèses 47, Soc.
Math. France (2015) 39 MR3525601
32
P G Goerss ,
J F Jardine , Simplicial homotopy
theory , 174, Birkhäuser (1999) MR1711612
33
A Grothendieck ,
Eléments de
géométrie algébrique, IV : Étude locale des schémas et des
morphismes de schémas, IV , Inst. Hautes Études Sci.
Publ. Math. 32 (1967) 5 MR0238860
34
S Hollander ,
A
homotopy theory for stacks , Israel J. Math. 163 (2008)
93 MR2391126
35
A Iarrobino ,
An
algebraic fibre bundle over P 1 that
is not a vector bundle , Topology 12 (1973) 229 MR0340254
36
J F Jardine ,
On
the homotopy groups of algebraic groups , J. Algebra 81
(1983) 180 MR696133
37
M A Knus ,
Quadratic and
Hermitian forms over rings , 294, Springer (1991)
MR1096299
38
M I Krusemeyer ,
Fundamental
groups, algebraic K –theory, and a
problem of Abhyankar , Invent. Math. 19 (1973) 15
MR0335522
39
T Y Lam ,
Serre’s
problem on projective modules , Springer (2006) MR2235330
40
B Margaux , The structure of the
group G ( k [ t ]) : variations on a theme of Soulé ,
Algebra Number Theory 3 (2009) 393 MR2525556
41
J S Milne ,
Étale cohomology , 33, Princeton Univ. Press (1980)
MR559531
42
J Milnor , D
Husemoller , Symmetric bilinear
forms , 73, Springer (1973) MR0506372
43
F Morel , On the
Friedlander–Milnor conjecture for groups of small rank ,
from: "Current developments in mathematics, 2010" (editors D
Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau),
International (2011) 45 MR2906371
44
F Morel , 𝔸 1 –algebraic topology over a field ,
2052, Springer (2012) MR2934577
45
F Morel , V
Voevodsky , A 1 –homotopy theory of schemes ,
Inst. Hautes Études Sci. Publ. Math. 90 (1999) 45 MR1813224
46
L F Moser ,
𝔸 1 –locality results for linear algebraic
groups , in preparation
47
L F Moser ,
Rational
triviale Torseure und die Serre–Grothendiecksche
Vermutung , Diplomarbeit, Ludwig-Maximilians-Universität
München (2008)
48
Y A Nisnevich ,
Espaces homogènes principaux rationnellement triviaux et
arithmétique des schémas en groupes réductifs sur les anneaux
de Dedekind , C. R. Acad. Sci. Paris Sér. I Math. 299 (1984)
5 MR756297
49
I Panin , Proof of
Grothendieck–Serre conjecture on principal G –bundles over regular local rings containing
a finite field , preprint (2014) arXiv:1406.0247
50
I Panin , C
Walter , On the motivic commutative ring spectrum
BO , preprint (2010) arXiv:1011.0650
51
I Panin , C
Walter , Quaternionic Grassmannians and Pontryagin
classes in algebraic geometry , preprint (2010) arXiv:1011.0649
52
V A Petrov ,
A K Stavrova , Elementary subgroups in isotropic
reductive groups , Algebra i Analiz 20 (2008) 160
MR2473747
53
D Popescu , Polynomial rings
and their projective modules , Nagoya Math. J. 113
(1989) 121 MR986438
54
D Quillen , Projective modules over
polynomial rings , Invent. Math. 36 (1976) 167 MR0427303
55
M S Raghunathan ,
Principal bundles on affine space , from: "C P Ramanujam
: a tribute" (editor K G Ramanathan), Tata Inst. Fund.
Res. Studies in Math. 8, Springer (1978) 187 MR541022
56
A Ramanathan ,
Deformations of
principal bundles on the projective line , Invent. Math.
71 (1983) 165 MR688263
57
M Schlichting ,
Euler
class groups and the homology of elementary and special linear
groups , Adv. Math. 320 (2017) 1 MR3709100
58
T A Springer ,
F D Veldkamp , Octonions, Jordan
algebras and exceptional groups , Springer (2000)
MR1763974
59
A Stavrova ,
Homotopy
invariance of non-stable K 1 –functors , J. K –Theory 13 (2014) 199 MR3189425
60
A A Suslin ,
Locally polynomial
rings and symmetric algebras , Izv. Akad. Nauk SSSR Ser.
Mat. 41 (1977) 503 MR0444647
61
R W Thomason ,
Equivariant
resolution, linearization, and Hilbert’s fourteenth problem
over arbitrary base schemes , Adv. in Math. 65 (1987) 16
MR893468
62
K Voelkel , M
Wendt , On 𝔸 1 –fundamental groups of isotropic
reductive groups , C. R. Math. Acad. Sci. Paris 354
(2016) 453 MR3488111
63
C A Weibel ,
Homotopy
algebraic K –theory , from:
"Algebraic K –theory and algebraic
number theory" (editors M R Stein, R K Dennis),
Contemp. Math. 83, Amer. Math. Soc. (1989) 461 MR991991
64
M Wendt , 𝔸 1 –homotopy of Chevalley groups , J.
K –Theory 5 (2010) 245 MR2640204
65
M Wendt , Rationally trivial
torsors in 𝔸 1 –homotopy theory , J. K –Theory 7 (2011) 541 MR2811715
66
G W Whitehead ,
On mappings
into group-like spaces , Comment. Math. Helv. 28 (1954)
320 MR0065927