Tunisian Journal of Mathematics

Ramification groups of coverings and valuations

Takeshi Saito

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Abstract

We give a purely scheme theoretic construction of the filtration by ramification groups of the Galois group of a covering. The valuation need not be discrete but the normalizations are required to be locally of complete intersection.

Article information

Source
Tunisian J. Math., Volume 1, Number 3 (2019), 373-426.

Dates
Received: 8 January 2018
Revised: 8 May 2018
Accepted: 23 May 2018
First available in Project Euclid: 15 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.tunis/1544842820

Digital Object Identifier
doi:10.2140/tunis.2019.1.373

Mathematical Reviews number (MathSciNet)
MR3907745

Zentralblatt MATH identifier
07027460

Subjects
Primary: 14B25: Local structure of morphisms: étale, flat, etc. [See also 13B40]
Secondary: 11S15: Ramification and extension theory

Keywords
ramification groups valuation rings

Citation

Saito, Takeshi. Ramification groups of coverings and valuations. Tunisian J. Math. 1 (2019), no. 3, 373--426. doi:10.2140/tunis.2019.1.373. https://projecteuclid.org/euclid.tunis/1544842820


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References

  • A. Abbes and T. Saito, “Ramification of local fields with imperfect residue fields”, Amer. J. Math. 124:5 (2002), 879–920.
  • A. Abbes and T. Saito, “Ramification and cleanliness”, Tohoku Math. J. $(2)$ 63:4 (2011), 775–853.
  • S. Bosch, W. Lütkebohmert, and M. Raynaud, “Formal and rigid geometry, IV: The reduced fibre theorem”, Invent. Math. 119:2 (1995), 361–398.
  • N. Bourbaki, Éléments de mathématique: Algébre commutative, chapitres 5 á 7, Masson, Paris, 1985.
  • A. Grothendieck and J. A. Dieudonné, “Eléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas, I”, Inst. Hautes Études Sci. Publ. Math. 20 (1964), 5–259.
  • A. Grothendieck, “Eléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas, II”, Inst. Hautes Études Sci. Publ. Math. 24 (1965), 5–231.
  • A. Grothendieck, “Eléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas, III”, Inst. Hautes Études Sci. Publ. Math. 28 (1966), 5–255.
  • A. Grothendieck, “Eléments de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas, IV”, Inst. Hautes Études Sci. Publ. Math. 32 (1967), 5–361.
  • K. Fujiwara and F. Kato, Foundations of rigid geometry, I, European Mathematical Society, Zürich, 2018.
  • M. Raynaud and L. Gruson, “Critères de platitude et de projectivité: techniques de “platification” d'un module”, Invent. Math. 13 (1971), 1–89.
  • T. Saito, “Wild ramification and the characteristic cycle of an $l$-adic sheaf”, J. Inst. Math. Jussieu 8:4 (2009), 769–829.
  • J.-P. Serre, Corps locaux, 2ième ed., Publications de l'Université de Nancago VIII, Hermann, Paris, 1968.
  • A. Grothendieck, Revêtements étales et groupe fondamental (Séminaire de Géométrie Algébrique du Bois Marie 1960–1961), Lecture Notes in Math. 224, Springer, 1971.
  • P. Deligne, “Cohomologie étale, les points de départ”, pp. 4–75 in Cohomologie étale (Séminaire de Géométrie Algébrique du Bois Marie), edited by P. Deligne, Lecture Notes in Math. 569, Springer, 1977.
  • P. Deligne, “La formule de Picard–Lefschetz”, pp. [exposé] XV, pp. 165–196 in Groupes de monodromie en géométrie algébrique, II: Exposés X–XXII (Séminaire de Géométrie Algébrique du Bois Marie 1967–1969), edited by P. Deligne and N. Katz, Lecture Notes in Math. 340, Springer, 1973.
  • M. Temkin, “Relative Riemann–Zariski spaces”, Israel J. Math. 185 (2011), 1–42.