The tame site of a scheme

Springer Science and Business Media LLC - Tập 223 - Trang 379-443 - 2020
Katharina Hübner1, Alexander Schmidt2
1Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Giv’at Ram, Jerusalem, Israel
2Mathematisches Institut, Universität Heidelberg, Heidelberg, Germany

Tài liệu tham khảo

Grothendieck, A., Murre, J.P.: The Tame Fundamental Group of a Formal Neighbourhood of a Divisor with Normal Crossings on a Scheme. Lecture Notes in Mathematics, vol. 208. Springer, Berlin (1971) Kerz, M., Schmidt, A.: On different notions of tameness in arithmetic geometry. Math. Ann. 346, 641–668 (2010) Achinger, P.: Wild ramification and \(K(\pi, 1)\) spaces. Invent. Math. 210(2), 453–499 (2017) Hübner, K.: The adic tame site (2018). arXiv:1801.04776 [math.AG] Hübner, K.: Tame and strongly etale cohomology of curves (2020). arXiv:1911.05595 [math.AG] Artin, M.: On the joins of Hensel rings. Adv. Math. 7, 282–296 (1971) Temkin, M.: Relative Riemann–Zariski spaces. Israel J. Math. 185, 1–42 (2011) Suslin, A., Voevodsky, V.: Singular homology of abstract algebraic varieties. Invent. Math. 123(1), 61–94 (1996) Geisser, T., Schmidt, A.: Tame class field theory for singular varieties over algebraically closed fields. Doc. Math. 21, 91–123 (2016) Engler, A., Prestel, A.: Valued Fields. Springer Monographs in Mathematics. Springer, Berlin (2005) Raynaud, M.: Anneaux Locaux Henséliens. Lecture Notes in Mathematics, vol. 169. Springer, Berlin (1970) Artin, M.: Grothendieck Topologies. Harvard University, Cambridge (1962) Grothendieck, A.: Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas IV. Inst. Hautes Études Sci. Publ. Math. 32, 361 (1967) The Stacks Project Authors. The Stacks Project. https://stacks.math.columbia.edu. Accessed 19 Apr 2020 Schmidt, A.: On quasi-purity of the branch locus. Manuscr. Math. 161(3–4), 325–331 (2020) Huber, R.: Étale Cohomology of Rigid Analytic Varieties and Adic Spaces. Aspects of Mathematics. Vieweg, Brunswick (1996) Hochster, M.: Prime ideal structure in commutative rings. Trans. Am. Math. Soc. 142, 43–60 (1969) Huber, R.: Continuous valuations. Math. Z. 212, 455–477 (1993) Artin, M., Grothendieck, A., Verdier, J.-L.: Théorie de topos et cohomologie étale des schémas (SGA 4). Séminaire de géométrie algébrique du Bois-Marie—1963–1964. Springer, Berlin (1972) Artin, M., Mazur, B.: Etale Homotopy. Springer, Berlin (1969) Demazure, M., Grothendieck, A.: Schémas en groupes (SGA 3). Séminaire de géometrie algébrique du Bois Marie—1962–1964. Springer, Berlin (1970) Kerz, M., Schmidt, A.: Covering data and higher dimensional global class field theory. J. Number Theory 129(10), 2569–2599 (2009) Schmidt, A.: Singular homology of arithmetic schemes. Algebra Number Theory 1(2), 183–222 (2007) Bhatt, B., Scholze, P.: The pro-étale topology for schemes. Astérisque 369, 99–201 (2015) Neukirch, J., Schmidt, A., Wingberg, K.: Cohomology of Number Fields, Volume 323 of Grundlehren der Mathematischen Wissenschaften, vol. 2. Springer, Berlin (2008) Mazur, B.: Notes on étale cohomology of number fields. Ann. Sci. Éc. Norm. Sup. (4) 6(521–552), 1973 (1974) Huber, R., Knebusch, M.: On valuation spectra. Contemp. Math. 155, 167–206 (1994) Conrad, B.: Deligne’s notes on Nagata compactifications. J. Ramanujan Math. Soc. 22(3), 205–257 (2007) Temkin, M., Tyomkin, I.: On relative birational geometry and Nagata’s compactification for algebraic spaces. Int. Math. Res. Not. IMRN 11, 3342–3387 (2018) Grothendieck, A.: Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II. Inst. Hautes Études Sci. Publ. Math. 24, 231 (1965) Milne, J.S.: Values of zeta functions of varieties over finite fields. Am. J. Math. 108(2), 297–360 (1986) Fujiwara, K.: A proof of the absolute purity conjecture (after Gabber). In: Usui, S., Green, M., Illusie, L., Kato, K., Looijenga, E., Mukai, S., Saito, S. (eds.) Algebraic Geometry 2000, Azumino (Hotaka), Volume 36 of Search Results Web results Advanced Studies in Pure Mathematics, pp. 153–183. Math. Soc., Tokyo (2002) Milne, J.S.: Étale Cohomology. Princeton Mathematical Series, vol. 33. Princeton University Press, Princeton (1980) Mazza, C., Voevodsky, V., Weibel, C.: Lecture Notes on Motivic Cohomology, Volume 2 of Clay Mathematics Monographs. American Mathematical Society, Providence, Clay Mathematics Institute, Cambridge (2006) Cisinski, D.-C., Déglise, F.: Triangulated Categories of Mixed Motives. Springer Monographs in Mathematics. Springer, Cham (2019) Suslin, A., Voevodsky, V.: Relative cycles and Chow sheaves. In: Voevodsky, V., Suslin, A., Friedlander, E.M. (eds.) Cycles, Transfers, and Motivic Homology Theories, Volume 143 of Annals of Mathematics Studies, pp. 10–86. Princeton Univ. Press, Princeton (2000) Voevodsky, V.: Triangulated categories of motives over a field. In: Voevodsky, V., Suslin, A., Friedlander, E.M. (eds.) Cycles, Transfers, and Motivic Homology Theories, Volume 143 of Annals of Mathematics Studies, pp. 188–238. Princeton Univ. Press, Princeton (2000)