Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
Book Information:
Authors:
David Eisenbud and
Joe Harris
Title:
The geometry of schemes
Additional book information:
Springer-Verlag,
New York,
2000,
x + 294 pp.,
ISBN 0-387-98638-3,
$69.95$
[Art] Artin M., The implicit function theorem in algebraic geometry, ``Algebraic Geometry. Bombay 1968'', Oxford Univ. Press (1969), 13-34. MR 0262237
[Da1] Danilov V., Algebraic varieties and schemes, in ``Algebraic Geometry, I'', Encyclopaedia Math. Sci., 23, Springer, Berlin (1994), 167-297. MR 1287420
[Da2] Danilov V., Cohomology of algebraic varieties, in ``Algebraic Geometry, II'', Encyclopaedia Math. Sci., 35, Springer, Berlin (1996), 1-125. CMP 96:13
[DM] Deligne P., Mumford D., The irreducibility of the space of curves of given genus, Publ. Math. Inst. Hautes Études Sci. 36 (1969), 75-109. MR 0262240
[EH] Eisenbud D., Harris J., Schemes: The Language of Modern Algebraic Geometry, Wadsworth and Brooks/Cole, Pacific Grove, California, 1992. MR 1166800
[Gel] Gelfand I., Ideale und primäre Ideale in normierten Ringen, Mat. Sbornik, N.S. 9(51) (1941), 41-48. MR 3:52a
[EGA1] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, I: Le langage des schémas, Publ. Math. Inst. Hautes Études Sci. 4 (1960), 1-228. MR 29:1207
[EGA2] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, II: Étude globale élementaire de quelques classes de morphismes, Publ. Math. Inst. Hautes Études Sci. 8 (1961), 1-222. MR 29:1208
[EGA3
] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents (premiére partie), Publ. Math. Inst. Hautes Études Sci. 11 (1961), 1-167. MR 29:1209
[EGA3
] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents (seconde partie), Publ. Math. Inst. Hautes Études Sci. 17 (1963), 1-91. MR 0163911
[EGA4
] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (premiére partie), Publ. Math. Inst. Hautes Études Sci. 20 (1964), 1-259. MR 0173675
[EGA4
] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (seconde partie), Publ. Math. Inst. Hautes Études Sci. 24 (1965), 1-231. MR 0199181
[EGA4
] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (troisième partie), Publ. Math. Inst. Hautes Études Sci. 28 (1966), 1-255. MR 0217086
[EGA4
] Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (quatrième partie), Publ. Math. Inst. Hautes Études Sci. 32 (1967), 1-361. MR 0238860
[SGA1] Grothendieck A. et al., Rev
tements étales et Groupe Fondamental, Lecture Notes in Math. 224, Springer-Verlag, Heidelberg, 1971. MR 0354651
[SGA2] Grothendieck A. et al., Cohomologie Locale des Faisceaux Cohérents et Théorème de Lefschetz Locale et Globaux, North-Holland, Amsterdam, 1968. MR 0476737
[SGA3] Grothendieck A. et al., Schémas en Groupes, I, II, III, Lecture Notes in Math. 151-153, Springer-Verlag, Heidelberg, 1970. MR 0274458; MR 43:223b; MR 43:223c
[SGA4] Grothendieck A. et al., Théorie des Topos et Cohomologie Étale des Schémas, Lecture Notes in Math. 269, 270, 305, Springer-Verlag, Heidelberg, 1972-73. MR 0354652; MR 50:7131; MR 0354654
[SGA4
] Deligne P. et al., Cohomologie Étale, Lecture Notes in Math. 569, Springer-Verlag, Heidelberg, 1977. MR 0463174
[SGA5] Grothendieck A. et al., Cohomologie l-adique et fonctions L, Lecture Notes in Math. 589, Springer-Verlag, Heidelberg, 1977. MR 0491704
[SGA6] Grothendieck A. et al., Théorie des intersections et Théorème de Riemann-Roch, Lecture Notes in Math. 225, Springer-Verlag, Heidelberg, 1971. MR 0354655
[SGA7I] Grothendieck A. et al., Groupes de Monodromie en Géometrie Algébrique, Part I, Lecture Notes in Math. 288, Springer-Verlag, Heidelberg, 1972. MR 0354656
[SGA7II] Deligne P. , Katz N., Groupes de Monodromie en Géometrie Algébrique, Part II, Lecture Notes in Math. 340, Springer-Verlag, Heidelberg, 1973. MR 0354657
[Harr] Harris J., Algebraic Geometry: A first course, Springer, New-York, 1992. MR 1182558
[Har] Hartshorne R., Algebraic Geometry, Springer-Verlag, New York, 1977. MR 0463157
[Hir] Hironaka H., Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. (2) 79 (1964), 109-203; Ann. Math. 4 (1960), 1-228. MR 0199184
[Jac] Jacobson N., A topology for the set of primitive ideals in an arbitrary ring, Proc. Nat. Acad. Sci. USA 31 (1945), 333-338. MR 7:110f
[Moi] Moishezon B., An algebraic analogue of compact complex spaces with a sufficiently large field of meromorphic functions. I, II, III, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 174-238, 323-367, 506-548.
[Mu1] Mumford D., Lectures on Curves on an Algebraic Surface, Ann. Math. Studies, v. 59, Princeton Univ. Press, 1966. MR 0209285
[Mu2] Mumford D., The red book of varieties and schemes, Lecture Notes in Math. 1358, Springer-Verlag, Berlin, 1988. MR 0971985
[Ser] Serre J.-P., Faisceaux algébriques cohérents, Ann. Math. 61 (1955), 197-278. MR 16:953c
[Sha] Shafarevich I., Basic Algebraic Geometry. I. Varieties in projective space (second edition), Springer-Verlag, New York, 1994. MR 1328833
[St1] Stone M., The theory of representations for Boolean algebras, Trans. Math. Math. Soc. 40 (1936), 37-111. CMP 95:18
[St2] Stone M., Applications of the theory of Boolean rings to general topology, Trans. Math. Math. Soc. 41 (1937), 375-481. CMP 95:18
[We1] Weil A., Foundations of Algebraic Geometry, A.M.S., New York, 1946. MR 9:303c
[We2] Weil A., Fibre-spaces in Algebraic Geometry (notes by A. Wallace), Chicago Univ., 1952.
[Zar] Zariski O., The compactness of the Riemann manifold of an abstract field of algebraic functions, Bull. Amer. Math. Soc. 50 (1944), 683-691. MR 6:186b
- [Art]
- Artin M., The implicit function theorem in algebraic geometry, ``Algebraic Geometry. Bombay 1968'', Oxford Univ. Press (1969), 13-34. MR 0262237
- [Da1]
- Danilov V., Algebraic varieties and schemes, in ``Algebraic Geometry, I'', Encyclopaedia Math. Sci., 23, Springer, Berlin (1994), 167-297. MR 1287420
- [Da2]
- Danilov V., Cohomology of algebraic varieties, in ``Algebraic Geometry, II'', Encyclopaedia Math. Sci., 35, Springer, Berlin (1996), 1-125. CMP 96:13
- [DM]
- Deligne P., Mumford D., The irreducibility of the space of curves of given genus, Publ. Math. Inst. Hautes Études Sci. 36 (1969), 75-109. MR 0262240
- [EH]
- Eisenbud D., Harris J., Schemes: The Language of Modern Algebraic Geometry, Wadsworth and Brooks/Cole, Pacific Grove, California, 1992. MR 1166800
- [Gel]
- Gelfand I., Ideale und primäre Ideale in normierten Ringen, Mat. Sbornik, N.S. 9(51) (1941), 41-48. MR 3:52a
- [EGA1]
- Grothendieck A., Dieudonné J., Élements de géométrie algébrique, I: Le langage des schémas, Publ. Math. Inst. Hautes Études Sci. 4 (1960), 1-228. MR 29:1207
- [EGA2]
- Grothendieck A., Dieudonné J., Élements de géométrie algébrique, II: Étude globale élementaire de quelques classes de morphismes, Publ. Math. Inst. Hautes Études Sci. 8 (1961), 1-222. MR 29:1208
- [EGA3
] - Grothendieck A., Dieudonné J., Élements de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents (premiére partie), Publ. Math. Inst. Hautes Études Sci. 11 (1961), 1-167. MR 29:1209
- [EGA3
] - Grothendieck A., Dieudonné J., Élements de géométrie algébrique, III: Étude cohomologique des faisceaux cohérents (seconde partie), Publ. Math. Inst. Hautes Études Sci. 17 (1963), 1-91. MR 0163911
- [EGA4
] - Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (premiére partie), Publ. Math. Inst. Hautes Études Sci. 20 (1964), 1-259. MR 0173675
- [EGA4
] - Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (seconde partie), Publ. Math. Inst. Hautes Études Sci. 24 (1965), 1-231. MR 0199181
- [EGA4
] - Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (troisième partie), Publ. Math. Inst. Hautes Études Sci. 28 (1966), 1-255. MR 0217086
- [EGA4
] - Grothendieck A., Dieudonné J., Élements de géométrie algébrique, IV: Étude locale des schémas et des morphismes de schémas (quatrième partie), Publ. Math. Inst. Hautes Études Sci. 32 (1967), 1-361. MR 0238860
- [SGA1]
- Grothendieck A. et al., Rev
tements étales et Groupe Fondamental, Lecture Notes in Math. 224, Springer-Verlag, Heidelberg, 1971. MR 0354651
- [SGA2]
- Grothendieck A. et al., Cohomologie Locale des Faisceaux Cohérents et Théorème de Lefschetz Locale et Globaux, North-Holland, Amsterdam, 1968. MR 0476737
- [SGA3]
- Grothendieck A. et al., Schémas en Groupes, I, II, III, Lecture Notes in Math. 151-153, Springer-Verlag, Heidelberg, 1970. MR 0274458; MR 43:223b; MR 43:223c
- [SGA4]
- Grothendieck A. et al., Théorie des Topos et Cohomologie Étale des Schémas, Lecture Notes in Math. 269, 270, 305, Springer-Verlag, Heidelberg, 1972-73. MR 0354652; MR 50:7131; MR 0354654
- [SGA4
] - Deligne P. et al., Cohomologie Étale, Lecture Notes in Math. 569, Springer-Verlag, Heidelberg, 1977. MR 0463174
- [SGA5]
- Grothendieck A. et al., Cohomologie l-adique et fonctions L, Lecture Notes in Math. 589, Springer-Verlag, Heidelberg, 1977. MR 0491704
- [SGA6]
- Grothendieck A. et al., Théorie des intersections et Théorème de Riemann-Roch, Lecture Notes in Math. 225, Springer-Verlag, Heidelberg, 1971. MR 0354655
- [SGA7I]
- Grothendieck A. et al., Groupes de Monodromie en Géometrie Algébrique, Part I, Lecture Notes in Math. 288, Springer-Verlag, Heidelberg, 1972. MR 0354656
- [SGA7II]
- Deligne P. , Katz N., Groupes de Monodromie en Géometrie Algébrique, Part II, Lecture Notes in Math. 340, Springer-Verlag, Heidelberg, 1973. MR 0354657
- [Harr]
- Harris J., Algebraic Geometry: A first course, Springer, New-York, 1992. MR 1182558
- [Har]
- Hartshorne R., Algebraic Geometry, Springer-Verlag, New York, 1977. MR 0463157
- [Hir]
- Hironaka H., Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II. Ann. of Math. (2) 79 (1964), 109-203; Ann. Math. 4 (1960), 1-228. MR 0199184
- [Jac]
- Jacobson N., A topology for the set of primitive ideals in an arbitrary ring, Proc. Nat. Acad. Sci. USA 31 (1945), 333-338. MR 7:110f
- [Moi]
- Moishezon B., An algebraic analogue of compact complex spaces with a sufficiently large field of meromorphic functions. I, II, III, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 174-238, 323-367, 506-548.
- [Mu1]
- Mumford D., Lectures on Curves on an Algebraic Surface, Ann. Math. Studies, v. 59, Princeton Univ. Press, 1966. MR 0209285
- [Mu2]
- Mumford D., The red book of varieties and schemes, Lecture Notes in Math. 1358, Springer-Verlag, Berlin, 1988. MR 0971985
- [Ser]
- Serre J.-P., Faisceaux algébriques cohérents, Ann. Math. 61 (1955), 197-278. MR 16:953c
- [Sha]
- Shafarevich I., Basic Algebraic Geometry. I. Varieties in projective space (second edition), Springer-Verlag, New York, 1994. MR 1328833
- [St1]
- Stone M., The theory of representations for Boolean algebras, Trans. Math. Math. Soc. 40 (1936), 37-111. CMP 95:18
- [St2]
- Stone M., Applications of the theory of Boolean rings to general topology, Trans. Math. Math. Soc. 41 (1937), 375-481. CMP 95:18
- [We1]
- Weil A., Foundations of Algebraic Geometry, A.M.S., New York, 1946. MR 9:303c
- [We2]
- Weil A., Fibre-spaces in Algebraic Geometry (notes by A. Wallace), Chicago Univ., 1952.
- [Zar]
- Zariski O., The compactness of the Riemann manifold of an abstract field of algebraic functions, Bull. Amer. Math. Soc. 50 (1944), 683-691. MR 6:186b
Review Information:
Reviewer:
Igor Dolgachev
Affiliation:
University of Michigan
Email:
idolga@math.ISA.umich.edu
Journal:
Bull. Amer. Math. Soc.
38 (2001), 467-473
Published electronically:
June 12, 2001
Review copyright:
© Copyright 2001
American Mathematical Society