Geometry & Topology Volume 21, issue 5 (2017)

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ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

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Kato–Nakayama spaces, infinite root stacks and the profinite homotopy type of log schemes

David Carchedi, Sarah Scherotzke, Nicolò Sibilla and Mattia Talpo

Geometry & Topology 21 (2017) 3093–3158

DOI: 10.2140/gt.2017.21.3093

Bibliography

1	D Abramovich, Q Chen, D Gillam, Y Huang, M Olsson, M Satriano, S Sun, Logarithmic geometry and moduli, from: "Handbook of moduli, I" (editors G Farkas, I Morrison), Adv. Lect. Math. 24, International Press (2013) 1 MR3184161
2	M Artin, Algebraization of formal moduli, II : Existence of modifications, Ann. of Math. 91 (1970) 88 MR0260747
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 4₁ ), 269, Springer (1972) MR0354652
4	M Artin, A Grothendieck, J L Verdier, Théorie des topos et cohomologie étale des schémas, Tome 3 : Exposés IX–XIX (SGA 4₃ ), 305, Springer (1973) MR0354654
5	M Artin, B Mazur, Etale homotopy, 100, Springer (1969) MR0245577
6	I Barnea, Y Harpaz, G Horel, Pro-categories in homotopy theory, Algebr. Geom. Topol. 17 (2017) 567 MR3604386
7	P Belmans, A J de Jong, others, The Stacks project, http://stacks.math.columbia.edu, electronic reference (2005–)
8	J Bochnak, M Coste, M F Roy, Real algebraic geometry, 36, Springer (1998) MR1659509
9	N Borne, A Vistoli, Parabolic sheaves on logarithmic schemes, Adv. Math. 231 (2012) 1327 MR2964607
10	D Carchedi, Higher orbifolds and Deligne–Mumford stacks as structured infinity topoi, preprint (2013) arXiv:1312.2204
11	D Carchedi, On the étale homotopy type of higher stacks, preprint (2015) arXiv:1511.07830
12	D Carchedi, On the homotopy type of higher orbifolds and Haefliger classifying spaces, Adv. Math. 294 (2016) 756 MR3479577
13	B Conrad, Cohomological descent, preprint (2004)
14	T Coyne, B Noohi, Singular chains on topological stacks, I, Adv. Math. 303 (2016) 1190 MR3552548
15	D Dugger, D C Isaksen, Topological hypercovers and 𝔸¹–realizations, Math. Z. 246 (2004) 667 MR2045835
16	E M Friedlander, Fibrations in etale homotopy theory, Inst. Hautes Études Sci. Publ. Math. 42 (1973) 5 MR0366929
17	E M Friedlander, Étale homotopy of simplicial schemes, 104, Princeton Univ. Press (1982) MR676809
18	M Groth, A short course on ∞–categories, preprint (2010) arXiv:1007.2925
19	K Hagihara, Structure theorem of Kummer étale K–group, K–Theory 29 (2003) 75 MR2029756
20	A Henriques, D Gepner, Homotopy theory of orbispaces, preprint (2007) arXiv:math/0701916
21	K R Hofmann, Triangulation of locally semi-algebraic spaces, PhD thesis, University of Michigan (2009) MR2713888
22	M Hoyois, Higher Galois theory, preprint (2015) arXiv:1506.07155
23	L Illusie, K Kato, C Nakayama, Quasi-unipotent logarithmic Riemann–Hilbert correspondences, J. Math. Sci. Univ. Tokyo 12 (2005) 1 MR2126784
24	L Illusie, C Nakayama, T Tsuji, On log flat descent, Proc. Japan Acad. Ser. A Math. Sci. 89 (2013) 1 MR3017719
25	D C Isaksen, A model structure on the category of pro-simplicial sets, Trans. Amer. Math. Soc. 353 (2001) 2805 MR1828474
26	J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
27	K Kato, Logarithmic structures of Fontaine–Illusie, from: "Algebraic analysis, geometry, and number theory" (editor J I Igusa), Johns Hopkins Univ. Press (1989) 191 MR1463703
28	K Kato, C Nakayama, Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over C, Kodai Math. J. 22 (1999) 161 MR1700591
29	A Kock, I Moerdijk, Presentations of étendues, Cahiers Topologie Géom. Différentielle Catég. 32 (1991) 145 MR1142688
30	S Lojasiewicz, Triangulation of semi-analytic sets, Ann. Scuola Norm. Sup. Pisa 18 (1964) 449 MR0173265
31	J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
32	J Lurie, Derived algebraic geometry, XIII : Rational and p–adic homotopy theory, preprint (2011)
33	A Mathew, V Stojanoska, Fibers of partial totalizations of a pointed cosimplicial space, Proc. Amer. Math. Soc. 144 (2016) 445 MR3415610
34	J P McCammond, A general small cancellation theory, Internat. J. Algebra Comput. 10 (2000) 1 MR1752738
35	W Nizioł, K–theory of log-schemes, I, Doc. Math. 13 (2008) 505 MR2452875
36	B Noohi, Foundations of topological stacks, I, preprint (2005) arXiv:math/0503247
37	B Noohi, Homotopy types of topological stacks, Adv. Math. 230 (2012) 2014 MR2927363
38	A Ogus, Lectures on logarithmic algebraic geometry, lecture notes (2006)
39	M C Olsson, Logarithmic geometry and algebraic stacks, Ann. Sci. École Norm. Sup. 36 (2003) 747 MR2032986
40	G Quick, Profinite homotopy theory, Doc. Math. 13 (2008) 585 MR2466189
41	G Quick, Some remarks on profinite completion of spaces, from: "Galois–Teichmüller theory and arithmetic geometry" (editors H Nakamura, F Pop, L Schneps, A Tamagawa), Adv. Stud. Pure Math. 63, Math. Soc. Japan (2012) 413 MR3051250
42	D G Quillen, Some remarks on etale homotopy theory and a conjecture of Adams, Topology 7 (1968) 111 MR0227988
43	H Ruddat, N Sibilla, D Treumann, E Zaslow, Skeleta of affine hypersurfaces, Geom. Topol. 18 (2014) 1343 MR3228454
44	U Schreiber, Differential cohomology in a cohesive infinity-topos, preprint (2013) arXiv:1310.7930
45	J P Serre, Cohomologie galoisienne, 5, Springer (1965) MR0201444
46	M Shiota, Whitney triangulations of semialgebraic sets, Ann. Polon. Math. 87 (2005) 237 MR2208550
47	D Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. 100 (1974) 1 MR0442930
48	M Talpo, A Vistoli, Infinite root stacks and quasi-coherent sheaves on logarithmic schemes, preprint (2014) arXiv:1410.1164
49	B Toën, M Vaquié, Algébrisation des variétés analytiques complexes et catégories dérivées, Math. Ann. 342 (2008) 789 MR2443764