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

Article, Preprint, Other literature type English OPEN
David, Carchedi; Sarah, Scherotzke; Nicolò, Sibilla; Mattia, Talpo; (2017)
  • Publisher: MSP
  • Journal: issn: 1465-3060
  • Related identifiers: doi: 10.2140/gt.2017.21.3093
  • Subject: Mathematics - Category Theory | Geometry and Topology | log scheme | Kato–Nakayama space | profinite spaces | 14F35 | 55P60 | root stack | Mathematics - Algebraic Topology | 55U35 | étale homotopy type | topological stack | 14F35, 55P60, 55U35 | infinity category | Mathematics - Algebraic Geometry
    arxiv: Mathematics::K-Theory and Homology | Mathematics::Algebraic Topology | Mathematics::Group Theory

For a log scheme locally of finite type over $\mathbb{C}$, a natural candidate for its profinite homotopy type is the profinite completion of its Kato-Nakayama space. Alternatively, one may consider the profinite homotopy type of the underlying topological stack of its ... View more
  • References (49)
    49 references, page 1 of 5

    [1] Th´eorie des topos et cohomologie ´etale des sch´emas. Tome 1: Th´eorie des topos. Lecture Notes in Mathematics, Vol. 269. Springer-Verlag, Berlin, 1972. S´eminaire de G´eom´etrie Alg´ebrique du BoisMarie 1963-1964 (SGA 4), Dirig´e par M. Artin, A. Grothendieck, et J. L. Verdier. Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat.

    [2] D. Abramovich, Q. Chen, D. Gillam, Y. Huang, M. Olsson, M. Satriano, and S. Sun. Logarithmic geometry and moduli. In G. Farkas and H. Morrison, editors, Handbook of Moduli. International Press, 2013.

    [3] M. Artin. Algebraization of formal moduli. II. Existence of modifications. Ann. of Math. (2), 91:88-135, 1970.

    [4] M. Artin and B. Mazur. Etale homotopy, volume 100 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1986. Reprint of the 1969 original.

    [5] Ilan Barnea, Yonatan Harpaz, and Geoffroy Horel. Pro-categories in homotopy theory. arXiv:1507.01564, 2015.

    [6] Jacek Bochnak, Michel Coste, and Marie-Fran¸coise Roy. Real algebraic geometry, volume 36. Springer Science & Business Media, 2013.

    [7] Niels Borne and Angelo Vistoli. Parabolic sheaves on logarithmic schemes. Advances in Mathematics, 231(3-4):1327-1363, oct 2012.

    [8] David Carchedi. Higher orbifolds and Deligne-Mumford stacks as structured infinity topoi, 2014. arXiv:1312.2204.

    [9] David Carchedi. On the ´etale homotopy types of higher stacks. arXiv:1511.07830, 2015.

    [10] David Carchedi. On the homotopy type of higher orbifolds and Haefliger classifying spaces. Adv. Math., 294:756-818, 2016.

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