A note on regularity of Noetherian complete local rings of unequal characteristic

Furuya, Mamoru; Niitsuma, Hiroshi

Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, p. 166-168 / Harvested from Project Euclid

Résumé

Let $(R, \boldsymbol{m})$ be a Noetherian complete local ring with unequal characteristic, and let $(P, pP)$ be a discrete valuation ring contained in $R$. Then, under some assumptions of separability on the residue fields, the following conditions are equivalent: (1) $R$ is a regular local ring and $p \notin \boldsymbol{m}^2$. (2) The $\boldsymbol{m}$-adic higher differential algebra $\widehat{D}_t(R/P, \boldsymbol{m})$ is a polynomial ring over $R$ for some $t~(1 \leq t)$.

Publié le : 2002-10-14
Classification: Regular local ring, $\boldsymbol {m}$-adic higher differential algebra, 13N10, 13H05

@article{1148392613,
     author = {Furuya, Mamoru and Niitsuma, Hiroshi},
     title = {A note on regularity of Noetherian complete local rings of unequal characteristic},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {78},
     number = {10},
     year = {2002},
     pages = { 166-168},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392613}
}

Furuya, Mamoru; Niitsuma, Hiroshi. A note on regularity of Noetherian complete local rings of unequal characteristic. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp.  166-168. http://gdmltest.u-ga.fr/item/1148392613/