On the ramification theory of regular schemes

On the ramification theory of regular schemes
HTML articles powered by AMS MathViewer

by Zhao Hua Luo PDF

Proc. Amer. Math. Soc. 120 (1994), 339-343 Request permission

We prove a fundamental theorem on the ramification of morphisms of regular schemes, extending Dedekind’s theorem of different.

References

Shreeram Abhyankar, On the valuations centered in a local domain, Amer. J. Math. 78 (1956), 321–348. MR 82477, DOI 10.2307/2372519
V. I. Danilov, Decomposition of some birational morphisms, Izv. Akad. Nauk SSSR Ser. Mat. 44 (1980), no. 2, 465–477, 480 (Russian). MR 571105
Ernst Kunz, Die Primidealteiler der Differenten in allgemeinen Ringen, J. Reine Angew. Math. 204 (1960), 165–182 (German). MR 124348, DOI 10.1515/crll.1960.204.165

Kähler differentials

M. T. Sancho de Salas, Factorization theorem for birational morphisms and relations between the multiplicities, Géométrie algébrique et applications, I (La Rábida, 1984) Travaux en Cours, vol. 22, Hermann, Paris, 1987, pp. 211–218. MR 907915
Zhao Hua Luo, An invariant approach to the theory of logarithmic Kodaira dimension of algebraic varieties, Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 1, 319–323. MR 940496, DOI 10.1090/S0273-0979-1988-15657-1
Zhao Hua Luo, Ramification divisor of regular schemes, Algebraic geometry and algebraic number theory (Tianjin, 1989–1990) Nankai Ser. Pure Appl. Math. Theoret. Phys., vol. 3, World Sci. Publ., River Edge, NJ, 1992, pp. 77–91. MR 1301087
Zhao Hua Luo, Factorization of birational morphisms of regular schemes, Math. Z. 212 (1993), no. 4, 505–509. MR 1214040, DOI 10.1007/BF02571670
Teresa Sancho de Salas, Theorems of factorizations for birational morphisms, Compositio Math. 70 (1989), no. 3, 275–291. MR 1002046
Oscar Zariski and Pierre Samuel, Commutative algebra, Volume I, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, New Jersey, 1958. With the cooperation of I. S. Cohen. MR 0090581