Geometry & Topology Volume 30, issue 3 (2026)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Unipotent morphisms

Daniel Bragg, Jack Hall and Siddharth Mathur

Geometry & Topology 30 (2026) 929–958

DOI: 10.2140/gt.2026.30.929

Bibliography

1	D Abramovich, M Olsson, A Vistoli, Tame stacks in positive characteristic, Ann. Inst. Fourier (Grenoble) 58 (2008) 1057 MR2427954
2	J Alper, Good moduli spaces for Artin stacks, Ann. Inst. Fourier (Grenoble) 63 (2013) 2349 MR3237451
3	J Alper, Adequate moduli spaces and geometrically reductive group schemes, Algebr. Geom. 1 (2014) 489 MR3272912
4	M Artin, J S Milne, Duality in the flat cohomology of curves, Invent. Math. 35 (1976) 111 MR419450
5	A Asok, B Doran, On unipotent quotients and some 𝔸¹-contractible smooth schemes, Int. Math. Res. Pap. 2007 (2007) MR2335246
6	F Bruhat, J Tits, Groupes réductifs sur un corps local, II : Schémas en groupes. Existence d’une donnée radicielle valuée, Inst. Hautes Études Sci. Publ. Math. 60 (1984) 197 MR756316
7	B Conrad, Smooth linear algebraic groups over the dual numbers, MathOverflow question (2010)
8	M Demazure, A Grothendieck, Schémas en groupes, Tome I : Propriétés générales des schémas en groupes, Exposés I–VII (SGA 3_I ), 151, Springer (1970) MR0274458
9	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
10	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
11	N Deshmukh, A Hogadi, S Mathur, Quasi-affineness and the 1-resolution property, Int. Math. Res. Not. 2022 (2022) 2224 MR4373233
12	D Edidin, B Hassett, A Kresch, A Vistoli, Brauer groups and quotient stacks, Amer. J. Math. 123 (2001) 761 MR1844577
13	S Estrada, P A G Asensio, S Odabaşı, A Lazard-like theorem for quasi-coherent sheaves, Algebr. Represent. Theory 16 (2013) 1193 MR3079799
14	O Gabber, Some theorems on Azumaya algebras, from: "The Brauer group" (editors M Kervaire, M Ojanguren), Lecture Notes in Math. 844, Springer (1981) 129 MR611868
15	J Giraud, Cohomologie non abélienne, Band 179, Springer (1971) MR344253
16	P Gross, The resolution property of algebraic surfaces, Compos. Math. 148 (2012) 209 MR2881314
17	P Gross, Tensor generators on schemes and stacks, Algebr. Geom. 4 (2017) 501 MR3683505
18	A Grothendieck, Le groupe de Brauer, II : Théorie cohomologique, from: "Séminaire Bourbaki, 9", Soc. Math. France (1995) 287 MR1608805
19	J Hall, D Rydh, Algebraic groups and compact generation of their derived categories of representations, Indiana Univ. Math. J. 64 (2015) 1903 MR3436239
20	J Hall, D Rydh, Perfect complexes on algebraic stacks, Compos. Math. 153 (2017) 2318 MR3705292
21	M Hovey, Homotopy theory of comodules over a Hopf algebroid, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K-theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 261 MR2066503
22	A J de Jong, A result of Gabber, preprint (2003)
23	I Kaplansky, Modules over Dedekind rings and valuation rings, Trans. Amer. Math. Soc. 72 (1952) 327 MR46349
24	A Kresch, A Vistoli, On coverings of Deligne–Mumford stacks and surjectivity of the Brauer map, Bull. London Math. Soc. 36 (2004) 188 MR2026412
25	G Laumon, L Moret-Bailly, Champs algébriques, 39, Springer (2000) MR1771927
26	D Lazard, Sur les modules plats, C. R. Acad. Sci. Paris 258 (1964) 6313 MR168625
27	S Mathur, The resolution property via Azumaya algebras, J. Reine Angew. Math. 774 (2021) 93 MR4250478
28	S Mathur, Experiments on the Brauer map in high codimension, Algebra Number Theory 16 (2022) 747 MR4449398
29	S Mathur, S Schröer, The resolution property holds away from codimension three, Trans. Amer. Math. Soc. 376 (2023) 1041 MR4531668
30	S Mukai, Semi-homogeneous vector bundles on an Abelian variety, J. Math. Kyoto Univ. 18 (1978) 239 MR498572
31	T Oda, Vector bundles on an elliptic curve, Nagoya Math. J. 43 (1971) 41 MR318151
32	M Olsson, A boundedness theorem for Hom-stacks, Math. Res. Lett. 14 (2007) 1009 MR2357471
33	M Raynaud, Faisceaux amples sur les schémas en groupes et les espaces homogènes, 119, Springer (1970) MR260758
34	M Rosenlicht, On quotient varieties and the affine embedding of certain homogeneous spaces, Trans. Amer. Math. Soc. 101 (1961) 211 MR130878
35	D Rydh, Remarks on “The resolution property for schemes and stacks” by B Totaro, (2009)
36	D Rydh, Étale dévissage, descent and pushouts of stacks, J. Algebra 331 (2011) 194 MR2774654
37	D Rydh, Noetherian approximation of algebraic spaces and stacks, J. Algebra 422 (2015) 105 MR3272071
38	D Rydh, Approximation of sheaves on algebraic stacks, Int. Math. Res. Not. 2016 (2016) 717 MR3493431
39	D Rydh, Absolute noetherian approximation of algebraic stacks, preprint (2023) arXiv:2311.09208
40	D Schäppi, A characterization of categories of coherent sheaves of certain algebraic stacks, preprint (2012) arXiv:1206.2764
41	S Schröer, On non-projective normal surfaces, Manuscripta Math. 100 (1999) 317 MR1726231
42	S Schröer, G Vezzosi, Existence of vector bundles and global resolutions for singular surfaces, Compos. Math. 140 (2004) 717 MR2041778
43	, The Stacks project, (2005–)
44	J Tong, Unipotent groups over a discrete valuation ring (after Dolgachev–Weisfeiler), from: "Autour des schémas en groupes, III" (editors G Prasad, P Polo), Panor. Synthèses 47, Soc. Math. France (2015) 173 MR3525845
45	B Totaro, The resolution property for schemes and stacks, J. Reine Angew. Math. 577 (2004) 1 MR2108211