Formal groups and Hopf algebras over discrete rings
Authors:
Robert A. Morris and Bodo Pareigis
Journal:
Trans. Amer. Math. Soc. 197 (1974), 113-129
MSC:
Primary 14L05
DOI:
https://doi.org/10.1090/S0002-9947-1974-0366935-2
MathSciNet review:
0366935
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: A theory of formal schemes and groups over abitrary rings is presented. The flat formal schemes in this theory have coalgebras of distributions which behave in the usual way. Frobenius and Verschiebung maps are studied.
- [1] P. Cartier, Groupes algébriques et groupes formels, Colloq. Théorie des Groupes Algébriques (Bruxelles, 1962) Librairie Universitaire, Louvain; GauthierVillars, Paris, 1962, pp. 87–111 (French). MR 0148665
- [2] -, Groupes formels associés aux anneaux de Witt généralisés, C. R. Acad. Sci. Paris Sér. A--B 265 (1967), A49-A52. MR 36 #1448.
- [3] Michel Demazure and Pierre Gabriel, Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970 (French). Avec un appendice Corps de classes local par Michiel Hazewinkel. MR 0302656
- [4] P. Gabriel, Étude infinitésimale des schémas en groupes: Groupes formels, Exposé VIIB, Schémas en Groupes 1 (SGA 3) 1962/64, Lecture Notes in Math., vol. 151, Springer-Verlag, Berlin, 1970.
- [5] Robert G. Heyneman and Moss E. Sweedler, Affine Hopf algebras. II, J. Algebra 16 (1970), 271–297. MR 0265433, https://doi.org/10.1016/0021-8693(70)90032-3
- [6] Michel Lazard, Sur les groupes de Lie formels à un paramètre, Bull. Soc. Math. France 83 (1955), 251–274 (French). MR 0073925
- [7] Ju. I. Manin, Theory of commutative formal groups over fields of finite characteristic, Uspehi Mat. Nauk 18 (1963), no. 6 (114), 3–90 (Russian). MR 0157972
- [8] Robert A. Morris and Bodo Pareigis, Formal groups over discrete rings, Bull. Amer. Math. Soc. 79 (1973), 449–453. MR 0321937, https://doi.org/10.1090/S0002-9904-1973-13210-0
- [9] David Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, No. 5, Published for the Tata Institute of Fundamental Research, Bombay; Oxford University Press, London, 1970. MR 0282985
- [10] Moss E. Sweedler, Hopf algebras, Mathematics Lecture Note Series, W. A. Benjamin, Inc., New York, 1969. MR 0252485
Retrieve articles in Transactions of the American Mathematical Society with MSC: 14L05
Retrieve articles in all journals with MSC: 14L05
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1974-0366935-2
Article copyright:
© Copyright 1974
American Mathematical Society


