On étend le théorème de Hasse–Arf de la classe des extensions résiduellement séparables des anneaux de valuation discrète complets à la classe des extensions monogènes.
I extend the Hasse–Arf theorem from residually separable extensions of complete discrete valuation rings to monogenic extensions.
@article{JTNB_2004__16_2_373_0,
author = {Borger, James},
title = {A monogenic {Hasse-Arf} theorem},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {373--375},
publisher = {Universit\'e Bordeaux 1},
volume = {16},
number = {2},
year = {2004},
doi = {10.5802/jtnb.451},
zbl = {1077.13011},
mrnumber = {2143559},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.451/}
}
Borger, James. A monogenic Hasse-Arf theorem. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 2, pp. 373-375. doi : 10.5802/jtnb.451. http://www.numdam.org/articles/10.5802/jtnb.451/
[1] K. Kato, Swan conductors for characters of degree one in the imperfect residue field case. Algebraic -theory and algebraic number theory, ed. M. Stein and R. K. Dennis, Contemp. Math. 83, Amer. Math. Soc., Providence, 1989, 101–131. | MR | Zbl
[2] S. Matsuda, On the Swan conductor in positive characteristic. Amer. J. Math. 119 (1997), no. 4, 705–739. | MR | Zbl
[3] J-P. Serre, Corps locaux. Deuxième édition. Hermann, Paris, 1968. | MR | Zbl
[4] B. de Smit, The Different and Differentials of Local Fields with Imperfect Residue Fields. Proc. Edin. Math. Soc. 40 (1997), 353–365. | MR | Zbl
[5] L. Spriano. Thesis, Université de Bordeaux, 1999.
Cité par Sources :
