Algèbre homologique, Géométrie algébrique
Descent for coherent sheaves along formal/open coverings
Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 577-594.

For a regular Noetherian scheme X with a divisor with strict normal crossings D we prove that coherent sheaves satisfy descent w.r.t. the “covering” consisting of the open parts in the various completions of X along the components of D and their intersections.

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DOI : 10.5802/crmath.75
Classification : 14C20, 14B20, 18F20, 13J10
Hörmann, Fritz 1

1 Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Germany
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Hörmann, Fritz. Descent for coherent sheaves along formal/open coverings. Comptes Rendus. Mathématique, Tome 358 (2020) no. 5, pp. 577-594. doi : 10.5802/crmath.75. http://www.numdam.org/articles/10.5802/crmath.75/

[1] Beauville, Arnaud; Laszlo, Yves Un lemme de descente, C. R. Math. Acad. Sci. Paris, Volume 320 (1995) no. 3, pp. 335-340 | MR | Zbl

[2] Ben-Bassat, Oren; Temkin, Michael Berkovich spaces and tubular descent, Adv. Math., Volume 234 (2013), pp. 217-238 | DOI | MR | Zbl

[3] Bhatt, Bhargav Algebraization and Tannaka duality, Camb. J. Math., Volume 4 (2016) no. 4, pp. 403-461 | DOI | MR | Zbl

[4] Ferrand, Daniel; Raynaud, Michel Fibres formelles d’un anneau local noethérien, Ann. Sci. Éc. Norm. Supér., Volume 3 (1970), pp. 295-311 | DOI | Zbl

[5] Groechenig, Michael Adelic descent theory, Compos. Math., Volume 153 (2017) no. 8, pp. 1706-1746 | DOI | MR | Zbl

[6] Grothendieck, Alexander; Dieudonné, Jean A. Eléments de géométrie algébrique. I, Grundlehren der Mathematischen Wissenschaften, 166, Springer, 1971, ix+466 pages | Zbl

[7] Hörmann, Fritz Generalized automorphic sheaves and the proportionality principle of Hirzebruch–Mumford (2016) | arXiv

[8] Hörmann, Fritz Fibered multiderivators and (co)homological descent, Theory Appl. Categ., Volume 32 (2017) no. 38, pp. 1258-1362 | MR | Zbl

[9] Cohomologie l-adique et fonctions L (Illusie, Luc, ed.), Lecture Notes in Mathematics, 589, Springer, 1977, xii+484 pages Séminaire de Géometrie Algébrique du Bois-Marie 1965–1966 (SGA 5) | MR

[10] Moret-Bailly, Laurent Un problème de descente, Bull. Soc. Math. Fr., Volume 124 (1996) no. 4, pp. 559-585 | DOI | Numdam | MR | Zbl

[11] Schäppi, Daniel Descent via Tannaka duality (2015) | arXiv

[12] Serre, Jean-Pierre Faisceaux algébriques cohérents, Ann. Math., Volume 61 (1955), pp. 197-278 | DOI | Zbl

[13] The Stacks Project Authors Stacks project (2014) (Available at http://stacks.math.columbia.edu)

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