Taiwanese Journal of Mathematics

On Henselian Rigid Geometry

Fumiharu Kato

Full-text: Open access

Abstract

We overview some of the foundations of the so-called henselian rigid geometry, and show that henselian rigid geometry has many aspects, useful in applications, that one cannot expect in the usual rigid geometry. This is done by announcing a few characteristic results, one of which is an analogue of Zariski Main Theorem.

Article information

Source
Taiwanese J. Math., Volume 21, Number 3 (2017), 531-547.

Dates
First available in Project Euclid: 1 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1498874605

Digital Object Identifier
doi:10.11650/tjm/7989

Mathematical Reviews number (MathSciNet)
MR3661379

Zentralblatt MATH identifier
06871330

Subjects
Primary: 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem)
Secondary: 14A20: Generalizations (algebraic spaces, stacks)

Keywords
rigid geometry Henselian schemes

Citation

Kato, Fumiharu. On Henselian Rigid Geometry. Taiwanese J. Math. 21 (2017), no. 3, 531--547. doi:10.11650/tjm/7989. https://projecteuclid.org/euclid.twjm/1498874605


Export citation

References

  • N. Bourbaki, Elements of Mathematics, Commutative algebra, Translated from the French, Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass., 1972.
  • D. A. Cox, Algebraic tubular neighborhoods: I, II, Math. Scand. 42 (1978), no. 2, 211–228, 229–242. { https://doi.org/10.7146/math.scand.a-11750
  • K. Fujiwara, Theory of tubular neighborhood in étale topology, Duke Math. J. 80 (1995), no. 1, 15–57.
  • K. Fujiwara and F. Kato, Foundations of rigid geometry I, A book to appear in Monographs in Mathematics, European Mathematical Society Publishing House.
  • S. Greco, Henselization of a ring with respect to an ideal, Trans. Amer. Math. Soc. 144 (1969), 43–65.
  • S. Greco and R. Strano, Quasicoherent sheaves over affine Hensel schemes, Trans. Amer. Math. Soc. 268 (1981), no. 2, 445–465.
  • A. Grothendieck, Éléments de géométrie algébrique, Inst. Hautes Études Sci. Publ. Math. 4, 8, 11, 17, 20, 24, 28, 32, 1961–1967.
  • H. Kurke, G. Pfister and M. Roczen, Henselsche Ringe und algebraische Geometrie, Mathematische Monographien, Band II. VEB Deutscher Verlag der Wissenschaften, Berlin, 1975.
  • R. Maggioni, Il teorema di Chevalley per schemi formali e schemi henseliani, Riv. Mat. Univ. Parma (4) 10 (1984), 285–292.
  • R. Strano, On the affineness of Hensel schemes, in Commutative Algebra (Trento, 1981), 305–320, Lecture Notes in Pure and Appl. Math. 84, Dekker, New York, 1983.