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Unramified $F$–divided objects and the étale fundamental pro-groupoid in positive characteristic

Yuliang Huang, Giulio Orecchia and Matthieu Romagny

Geometry & Topology 26 (2022) 3221–3306
Bibliography
1 P Berthelot, A note on Frobenius divided modules in mixed characteristics, Bull. Soc. Math. France 140 (2012) 441 MR3059121
2 N Borne, A Vistoli, The Nori fundamental gerbe of a fibered category, J. Algebraic Geom. 24 (2015) 311 MR3311586
3 H Brenner, The affine class group of a normal scheme, Comm. Algebra 31 (2003) 2849 MR1986219
4 E Descotte, E J Dubuc, A theory of 2–pro-objects, Cah. Topol. Géom. Différ. Catég. 55 (2014) 2 MR3185522
5 T Dumitrescu, Reducedness, formal smoothness and approximation in characteristic p, Comm. Algebra 23 (1995) 1787 MR1323700
6 H Esnault, V Mehta, Simply connected projective manifolds in characteristic p > 0 have no nontrivial stratified bundles, Invent. Math. 181 (2010) 449 MR2660450
7 D Ferrand, Un adjoint, preprint to Fe20 (2019) arXiv:1902.05296
8 D Ferrand, Enveloppe étale de morphismes plats, Algebra Number Theory 16 (2022) 521 MR4449393
9 D Gieseker, Flat vector bundles and the fundamental group in non-zero characteristics, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 2 (1975) 1 MR382271
10 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
11 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, II, Inst. Hautes Études Sci. Publ. Math. 24 (1965) 5 MR0199181
12 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, III, Inst. Hautes Études Sci. Publ. Math. 28 (1966) 5 MR0217086
13 A Grothendieck, Éléments de géométrie algébrique, IV : Étude locale des schémas et des morphismes de schémas, IV, Inst. Hautes Études Sci. Publ. Math. 32 (1967) 5 MR0238860
14 A Grothendieck, Groupes de type multiplicatif : homomorphismes dans un schéma en groupes, from: "Schémas en groupes, Tome II : Groupes de type multiplicatif, et structure des schémas en groupes généraux (SGA 3II )" (editors M Demazure, A Grothendieck), Lecture Notes in Math. 152, Springer (1970) MR0274459
15 A Grothendieck, Foncteurs fibres, supports, étude cohomologique des morphismes finis, from: "Théorie des topos et cohomologie étale des schémas, Tome 2 (SGA 42 )" (editors M Artin, A Grothendieck, J L Verdier), Lecture Notes in Math. 270, Springer (1972) MR0354653
16 A Grothendieck, Revêtements étales et groupe fondamental (SGA 1), 3, Soc. Math. France (2003) MR2017446
17 A Grothendieck, J L Verdier, Préfaisceaux, from: "Théorie des topos et cohomologie étale des schémas, Tome 1 : Théorie des topos (SGA 41 )" (editors M Artin, A Grothendieck, J L Verdier), Lecture Notes in Math. 269, Springer (1972) MR0354652
18 J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
19 K Kato, Duality theories for the p–primary étale cohomology, I, from: "Algebraic and topological theories" (editors M Nagata, S Araki, A Hattori), Kinokuniya (1986) 127 MR1102256
20 E Kunz, Characterizations of regular local rings of characteristic p, Amer. J. Math. 91 (1969) 772 MR252389
21 J P May, Simplicial objects in algebraic topology, 11, Van Nostrand (1967) MR0222892
22 M Raynaud, Anneaux locaux henséliens, 169, Springer (1970) MR0277519
23 M Romagny, Composantes connexes et irréductibles en familles, Manuscripta Math. 136 (2011) 1 MR2820394
24 M Romagny, D Rydh, G Zalamansky, The complexity of a flat groupoid, Doc. Math. 23 (2018) 1157 MR3874949
25 M Rosenlicht, Some rationality questions on algebraic groups, Ann. Mat. Pura Appl. 43 (1957) 25 MR90101
26 J P P dos Santos, Fundamental group schemes for stratified sheaves, J. Algebra 317 (2007) 691 MR2362937
27 J P P dos Santos, Lifting D–modules from positive to zero characteristic, Bull. Soc. Math. France 139 (2011) 193 MR2828568
28 , The Stacks project, web reference (2005–)
29 F Tonini, L Zhang, Algebraic and Nori fundamental gerbes, J. Inst. Math. Jussieu 18 (2019) 855 MR3963521
30 F Tonini, L Zhang, F–divided sheaves trivialized by dominant maps are essentially finite, Trans. Amer. Math. Soc. 371 (2019) 5529 MR3937302
31 W C Waterhouse, Introduction to affine group schemes, 66, Springer (1979) MR547117