×

zbMATH — the first resource for mathematics

The divisor class group of the surface \(\exp(p^ n\cdot \log Z)=G(X,Y)\) over fields of characteristic \(p>0\). (English) Zbl 0528.14017

MSC:
14J25 Special surfaces
14C22 Picard groups
13F99 Arithmetic rings and other special commutative rings
13D99 Homological methods in commutative ring theory
14M05 Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal)
14C20 Divisors, linear systems, invertible sheaves
13B10 Morphisms of commutative rings
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Atiyah, M; Macdonald, I, Introduction to commutative algebra, (1969), Addison-Wesley Reading, Mass., · Zbl 0175.03601
[2] {\scK. Baba}, On p-radical descent of higher exponent, Osaka J. Math., in press. · Zbl 0478.13001
[3] {\scP. Blass}, Zariski surfaces, Dissertationes Math., in press. · Zbl 0523.14027
[4] {\scP. Blass}, Some geometric applications of a differential equation in characteristic p > 0 to the theory of algebraic surfaces, to appear. · Zbl 0561.14018
[5] Fossum, R, The divisor class group of a Krull domain, (1973), Springer-Verlag New York · Zbl 0256.13001
[6] Fujita, T, On the Zariski problem, (), No. 3
[7] {\scR. Ganong}, Plane Frobenius sandwiches, to appear. · Zbl 0504.13012
[8] Ganong, R, On plane curves with one place at infinity, J. reine angew. math., 307, 173-193, (1979) · Zbl 0398.14004
[9] Gould, H.W, Combinatorial identities, (1959-1960), Morgantown, W. Va.
[10] Griffiths; Harris, J, Principles of algebraic geometry, (1978), Wiley New York · Zbl 0408.14001
[11] Grothendieck, A, E.G.A, II IHES publ. math. no. 8, (1961)
[12] Hallier, N, Quelques propriétés arithmétiques des dérivations, C. R. acad. sci., 258, 6041-6044, (1964) · Zbl 0218.13004
[13] Hallier, N, Étude des dérivations de certains corps, C. R. acad. sci., 261, 3716-3718, (1965) · Zbl 0171.29601
[14] Hallier, N, Utilisation des groupes de cohomologie, C. R. acad. sci., 261, 3922-3924, (1965) · Zbl 0136.31903
[15] Hallier, N, Quelches propriétés d’une dérivation particulière, C. R. acad. sci., 262, 553-556, (1966) · Zbl 0166.30801
[16] Jacobson, N, ()
[17] {\scJ. Lang}, An example related to the affine theorem of Castelnuovo, Michigan Math. J., in press. · Zbl 0495.14021
[18] Lang, J, (), to appear
[19] {\scJ. Lang}, The divisor classes of the hypersurface zpm = G(x1,…,xn) in characteristic p > 0, Trans. Amer. Math. Soc., in press.
[20] Lipman, J, Desingularization of two dimensional schemes, Ann. of math., 107, 151-207, (1978) · Zbl 0349.14004
[21] {\scJ. Lipman}, “Rational Singularities,” IHES, Publ. Math. No. 36. · Zbl 0405.14010
[22] Matsumura, H, Commutative algebra, (1970), Benjamin New York · Zbl 0211.06501
[23] Miyanishi, M, Regular subrings of a polynomial ring, Osaka J. math., 17, (1980)
[24] Miyanishi, M; Sugie, T, Affine surfaces containing cylinderlike open sets, J. math. kyote univ., 20, (1980) · Zbl 0445.14017
[25] {\scM. Miyanishi and P. Russell}, Purely inseparable coverings of the affine plane of exponent one, to appear. · Zbl 0581.14007
[26] {\scP. Russell}, Hamburger-Noether expansion and approximate roots, to appear. · Zbl 0455.14018
[27] {\scP. Russell}, Affine ruled surfaces, Math. Ann., in press. · Zbl 0754.53016
[28] Samuel, P, Lectures on unique factorization domains, Tata lecture notes, (1964) · Zbl 0184.06601
[29] Samuel, P, Classes de diviseurs et derivées logarithmiques, (), 81-96 · Zbl 0127.26002
[30] Singh, B, On a conjecture of Samuel, Math. Z., 105, 157-159, (1968) · Zbl 0159.05104
[31] Yuan, S, On logarithmic derivatives, Bull. soc. math. France, 96, 41-52, (1968) · Zbl 0184.06801
[32] Zariski, O, On Castelnuovo’s criterion of rationality pa = pg = 0 of an algebraic surface, Illinois J. math., 2, No. 3, (1958)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.