Logarithmic geometry and algebraic stacks

Martin C. Olsson

Annales scientifiques de l'École Normale Supérieure (2003)

  • Volume: 36, Issue: 5, page 747-791
  • ISSN: 0012-9593

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Olsson, Martin C.. "Logarithmic geometry and algebraic stacks." Annales scientifiques de l'École Normale Supérieure 36.5 (2003): 747-791. <http://eudml.org/doc/82617>.

@article{Olsson2003,
author = {Olsson, Martin C.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Grothendieck topologies; étale topologies; sites; algebraic spaces; log structures; fibred categories},
language = {eng},
number = {5},
pages = {747-791},
publisher = {Elsevier},
title = {Logarithmic geometry and algebraic stacks},
url = {http://eudml.org/doc/82617},
volume = {36},
year = {2003},
}

TY - JOUR
AU - Olsson, Martin C.
TI - Logarithmic geometry and algebraic stacks
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2003
PB - Elsevier
VL - 36
IS - 5
SP - 747
EP - 791
LA - eng
KW - Grothendieck topologies; étale topologies; sites; algebraic spaces; log structures; fibred categories
UR - http://eudml.org/doc/82617
ER -

References

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  2. [2] Artin M., Bertin J.E., Demazure M., Gabriel P., Grothendieck A., Raynaud M., Serre J.-P., Schémas en groupes. Fasc. 1: Exposés 1 à 4, Institut des Hautes Études Scientifiques, Paris, 1963/1964. MR207702
  3. [3] Artin M., Grothendieck A., Verdier J.-L., Théorie des topos et cohomologie étale des schémas, in: Artin M., Grothendieck A., Verdier J.L. (Eds.), Séminaire de géométrie algébrique du Bois-Marie 1963–1964 (SGA 4), Lecture Notes in Mathematics, Vols. 269, 270, 305, Springer-Verlag, Berlin, 1972, Avec la collaboration de N. Bourbaki, P. Deligne et B. Saint-Donat. Zbl0237.00012MR354654
  4. [4] Dieudonné J., Grothendieck A., Éléments de géométrie algébrique, no. 4, 8, 11, 17, 20, 24, 28, 32, Inst. Hautes Études Sci. Publ. Math, Paris, 1961. Zbl0203.23301
  5. [5] Grothendieck A., Revêtements étale et groupe fondamental, Lecture Notes in Mathematics, vol. 224, Springer–Verlag, Berlin, 1971. MR354651
  6. [6] Hartshorne R., Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, Springer-Verlag, New York, 1977. Zbl0367.14001MR463157
  7. [7] Illusie L., Logarithmic spaces (according to K. Kato), in: Barsotti Symposium in Algebraic Geometry (Abano Terme, 1991), Academic Press, San Diego, CA, 1994, pp. 183-203. Zbl0832.14015MR1307397
  8. [8] Kato F., Log smooth deformation theory, Tôhoku Math. J. (2)48 (3) (1996) 317-354. Zbl0876.14007MR1404507
  9. [9] Kato K., Logarithmic structures of Fontaine-Illusie, in: Algebraic Analysis, Geometry, and Number Theory (Baltimore, MD, 1988), Johns Hopkins Univ. Press, Baltimore, MD, 1989, pp. 191-224. Zbl0776.14004MR1463703
  10. [10] Kato K., Logarithmic structures of Fontaine-Illusie II: Logarithmic flat topology (incomplete) preprint, 1991. MR1463703
  11. [11] Kato K., Log flat morphisms and neat charts, manuscript notes, 1991. 
  12. [12] Knutson D., Algebraic Spaces, Lecture Notes in Mathematics, vol. 203, Springer-Verlag, Berlin, 1971. Zbl0221.14001MR302647
  13. [13] Lafforgue L., Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math.147 (2002) 1-241. Zbl1038.11075MR1875184
  14. [14] Laumon G., Moret-Bailly L., Champs algébriques, Ergeb. Math.39 (2000). MR1771927
  15. [15] Milne J.S., Étale Cohomology, Princeton University Press, Princeton, NJ, 1980. Zbl0433.14012MR559531
  16. [16] Niziol W., Toric singularities: log-blow-ups and global resolutions, preprint, 1999. MR2177194
  17. [17] Ogus A., Lectures on logarithmic algebraic geometry, TeXed notes, 2001. 
  18. [18] Olsson M., Log algebraic stacks and moduli of log schemes, PhD Thesis, UC Berkeley, May 2001. 
  19. [19] Olsson M., Crystalline cohomology of schemes over algebraic stacks, preprint, 2002. 
  20. [20] Olsson M., Universal log structures on semi-stable varieties, Tôhoku Math. J.55 (2003) 397-438. Zbl1069.14015MR1993863

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