The cohomological dimension of the quotient field of the two dimensional complete local domain
Compositio Mathematica, Volume 79 (1991) no. 2, pp. 157-167.
@article{CM_1991__79_2_157_0,
author = {Kuzumaki, Takako},
title = {The cohomological dimension of the quotient field of the two dimensional complete local domain},
journal = {Compositio Mathematica},
pages = {157--167},
publisher = {Kluwer Academic Publishers},
volume = {79},
number = {2},
year = {1991},
zbl = {0731.13010},
mrnumber = {1117338},
language = {en},
url = {http://archive.numdam.org/item/CM_1991__79_2_157_0/}
}
TY  - JOUR
AU  - Kuzumaki, Takako
TI  - The cohomological dimension of the quotient field of the two dimensional complete local domain
JO  - Compositio Mathematica
PY  - 1991
DA  - 1991///
SP  - 157
EP  - 167
VL  - 79
IS  - 2
PB  - Kluwer Academic Publishers
UR  - http://archive.numdam.org/item/CM_1991__79_2_157_0/
UR  - https://zbmath.org/?q=an%3A0731.13010
UR  - https://www.ams.org/mathscinet-getitem?mr=1117338
LA  - en
ID  - CM_1991__79_2_157_0
ER  - 
%0 Journal Article
%A Kuzumaki, Takako
%T The cohomological dimension of the quotient field of the two dimensional complete local domain
%J Compositio Mathematica
%D 1991
%P 157-167
%V 79
%N 2
%I Kluwer Academic Publishers
%G en
%F CM_1991__79_2_157_0
Kuzumaki, Takako. The cohomological dimension of the quotient field of the two dimensional complete local domain. Compositio Mathematica, Volume 79 (1991) no. 2, pp. 157-167. http://archive.numdam.org/item/CM_1991__79_2_157_0/

[1] Abhyankar, S.; Resolution of singularities for arithmetical surfaces. In Arithmetical Algebraic Geometry, New York: Harper and Row, (1963), 111-152. | MR | Zbl

[2] Artin, M.; Dimension cohomologique: Premiers résultats, in SGA 4, Tome 3, Lecture Notes in Mathematics 305, (1973), 43-63. | Zbl

[3] Bloch, S. and Kato, K.; p-adic étale coholology. Publ. Math. I.H.E.S. 63 (1986) 107-152. | Numdam | MR | Zbl

[4] Gabber, O.; A lecture at I.H.E.S. on March in 1981.

[5] Hironaka, H.; Desingularization of excellent surface. Lecture at Advanced Seminar in Algebraic Geometry, Bowdoin College, Summer 1967, notes by Bruce Bennett.

[6] Kato, K.; A generalization of local class field theory by using K-groups, I. J. fac. Sci. Univ. Tokyo Sec. IA 26 (1979) 303-376: II Ibid 27 (1980) 602-683: III ibid 29 (1982) 31-34. | MR | Zbl

[7] Kato, K.; Galois cohomology of complete discrete valuation fields. Lecture Notes in Mathematics 967 (1982) 215-238. | MR | Zbl

[8] Kato, K. and Kuzumaki, T.; The dimension of fields and algebraic K-theory. Journal of Number Theory Vol. 24 No. 2 (1986) 229-244. | MR | Zbl

[9] Matumura, H.; Commutative Algebra. W. A. Benjamin Co., New York 2nd ed. (1980). | MR

[10] Merkuriev, A.S. and Suslin, A.A.; K-cohomology of Severi-Brauer variety and norm residue homomorphism. Math. USSA-Izv. 21 (1984) 307-340. | Zbl

[11] Milnor, J.; Introduction to algebraic K-theory. Ann. Math. Stud. 72 (1971). | MR | Zbl

[12] Saito, S.; Arithmetic on two dimensional local rings. Invent. Math. 85 (1986) 379-414. | EuDML | MR | Zbl

[13] Satz, S.S.; Profinite groups, arithmetic and geometry. Ann. Math. Stud. 67 (1972). | MR | Zbl

[14] Serre, J.-P.; Cohomologie Galoisienne. Lecture Notes in Mathematics 5 (1965). | MR | Zbl

[15] Serre, J.-P.; Sur la dimension cohomologique des groupes profinis. Topology 3 (1965) 413-420. | MR | Zbl