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Betti realization of varieties defined by formal Laurent series

Piotr Achinger and Mattia Talpo

Geometry & Topology 25 (2021) 1919–1978
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 (2013) 1 MR3184161
2 D Abramovich, M Temkin, Functorial factorization of birational maps for qe schemes in characteristic 0, Algebra Number Theory 13 (2019) 379 MR3927050
3 P Achinger, K(π,1) spaces in algebraic geometry, PhD thesis, University of California, Berkeley (2015)
4 P Achinger, A Ogus, Monodromy and log geometry, Tunis. J. Math. 2 (2020) 455 MR4041282
5 M Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969) 23 MR268188
6 M Artin, A Grothendieck, J L Verdier, Théorie des topos et cohomologie étale des schémas, Tome 2 : Exposés V–VIII (SGA 42 ), 270, Springer (1972) MR0354653
7 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
8 M Artin, B Mazur, Étale homotopy, 100, Springer (1969) MR0245577
9 J Ayoub, Note sur les opérations de Grothendieck et la réalisation de Betti, J. Inst. Math. Jussieu 9 (2010) 225 MR2602027
10 A Beilinson, p–adic periods and derived de Rham cohomology, J. Amer. Math. Soc. 25 (2012) 715 MR2904571
11 P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
12 V G Berkovich, Complex analytic vanishing cycles for formal schemes, preprint (2015)
13 J Berner, Étale homotopy theory of non-Archimedean analytic spaces, preprint (2017) arXiv:1708.03657
14 A Blanc, Topological K–theory of complex noncommutative spaces, Compos. Math. 152 (2016) 489 MR3477639
15 N Borne, A Vistoli, Parabolic sheaves on logarithmic schemes, Adv. Math. 231 (2012) 1327 MR2964607
16 S Bosch, Lectures on formal and rigid geometry, 2105, Springer (2014) MR3309387
17 S Bosch, U Güntzer, R Remmert, Non-Archimedean analysis : a systematic approach to rigid analytic geometry, 261, Springer (1984) MR746961
18 S Bosch, W Lütkebohmert, Formal and rigid geometry, I : Rigid spaces, Math. Ann. 295 (1993) 291 MR1202394
19 D Carchedi, On the étale homotopy type of higher stacks, preprint (2015) arXiv:1511.07830
20 D Carchedi, S Scherotzke, N Sibilla, M Talpo, Kato–Nakayama spaces, infinite root stacks and the profinite homotopy type of log schemes, Geom. Topol. 21 (2017) 3093 MR3687115
21 D Carchedi, S Scherotzke, N Sibilla, M Talpo, On the profinite homotopy type of log schemes, preprint (2019) arXiv:1905.06243
22 B Conrad, Deligne’s notes on Nagata compactifications, J. Ramanujan Math. Soc. 22 (2007) 205 MR2356346
23 D Dugger, D C Isaksen, Topological hypercovers and 𝔸1–realizations, Math. Z. 246 (2004) 667 MR2045835
24 W G Dwyer, D M Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980) 17 MR578563
25 E M Friedlander, Étale homotopy of simplicial schemes, 104, Princeton Univ. Press (1982) MR676809
26 K Fujiwara, A proof of the absolute purity conjecture (after Gabber), from: "Algebraic geometry" (editors S Usui, M Green, L Illusie, K Kato, E Looijenga, S Mukai, S Saito), Adv. Stud. Pure Math. 36, Math. Soc. Japan (2002) 153 MR1971516
27 K Fujiwara, F Kato, Foundations of rigid geometry, I, Eur. Math. Soc. (2018) MR3752648
28 P Gabriel, M Zisman, Calculus of fractions and homotopy theory, 35, Springer (1967) MR0210125
29 J Giraud, Cohomologie non abélienne, 179, Springer (1971) MR0344253
30 M Goresky, R MacPherson, Stratified Morse theory, 14, Springer (1988) MR932724
31 M Groth, A short course on –categories, preprint (2010) arXiv:1007.2925
32 A Huber, C Jörder, Differential forms in the h–topology, Algebr. Geom. 1 (2014) 449 MR3272910
33 L Illusie, An overview of the work of K Fujiwara, K Kato, and C Nakayama on logarithmic étale cohomology, from: "Cohomologies p–adiques et applications arithmétiques, II" (editors P Berthelot, J M Fontaine, L Illusie, K Kato, M Rapoport), Astérisque 279, Soc. Math. France (2002) 271 MR1922832
34 L Illusie, K Kato, C Nakayama, Quasi-unipotent logarithmic Riemann–Hilbert correspondences, J. Math. Sci. Univ. Tokyo 12 (2005) 1 MR2126784
35 J F Jardine, Simplicial presheaves, J. Pure Appl. Algebra 47 (1987) 35 MR906403
36 K Kato, C Nakayama, Log Betti cohomology, log étale cohomology, and log de Rham cohomology of log schemes over , Kodai Math. J. 22 (1999) 161 MR1700591
37 C Koppensteiner, The de Rham functor for logarithmic D–modules, Selecta Math. 26 (2020) MR4122246
38 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
39 J Lurie, Derived algebraic geometry, V: Structured spaces, preprint (2011)
40 F Morel, V Voevodsky, 𝔸1–homotopy theory of schemes, Inst. Hautes Études Sci. Publ. Math. 90 (1999) 45 MR1813224
41 C Nakayama, Logarithmic étale cohomology, Math. Ann. 308 (1997) 365 MR1457738
42 C Nakayama, Nearby cycles for log smooth families, Compos. Math. 112 (1998) 45 MR1622751
43 C Nakayama, A Ogus, Relative rounding in toric and logarithmic geometry, Geom. Topol. 14 (2010) 2189 MR2740645
44 A Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Inst. Hautes Études Sci. Publ. Math. 21 (1964) 128 MR179172
45 A Ogus, Lectures on logarithmic algebraic geometry, 178, Cambridge Univ. Press (2018) MR3838359
46 M Olsson, Kummer coverings and specialization, preprint (2017)
47 M Raynaud, Géométrie analytique rigide d’après Tate, Kiehl,, from: "Table ronde d’analyse non archimédienne", Bull. Soc. Math. France, Mém 39-40, Soc. Math. France (1974) 319 MR0470254
48 D Rydh, Submersions and effective descent of étale morphisms, Bull. Soc. Math. France 138 (2010) 181 MR2679038
49 J P Serre, Exemples de variétés projectives conjuguées non homéomorphes, C. R. Acad. Sci. Paris 258 (1964) 4194 MR166197
50 S Smale, A Vietoris mapping theorem for homotopy, Proc. Amer. Math. Soc. 8 (1957) 604 MR87106
51 A J Stewart, V Vologodsky, Motivic integral of K3 surfaces over a non-Archimedean field, Adv. Math. 228 (2011) 2688 MR2838055
52 A Suslin, V Voevodsky, Singular homology of abstract algebraic varieties, Invent. Math. 123 (1996) 61 MR1376246
53 M Talpo, A Vistoli, Infinite root stacks and quasi-coherent sheaves on logarithmic schemes, Proc. Lond. Math. Soc. 116 (2018) 1187 MR3805055
54 M Talpo, A Vistoli, The Kato–Nakayama space as a transcendental root stack, Int. Math. Res. Not. 2018 (2018) 6145 MR3867403
55 M Temkin, Functorial desingularization of quasi-excellent schemes in characteristic zero: the nonembedded case, Duke Math. J. 161 (2012) 2207 MR2957701
56 D Treumann, Is there a geometric realization of ((t))–varieties ?, MathOverflow question (2016)
57 D Treumann, Complex K–theory of mirror pairs, preprint (2019) arXiv:1909.03018
58 H Voskuil, Non-Archimedean Hopf surfaces, Sém. Théor. Nombres Bordeaux 3 (1991) 405 MR1149806