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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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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, $69.95$

References [Enhancements On Off] (What's this?)

[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$_1$]
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$_2$]
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$_1$]
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$_2$]
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$_3$]
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$_4$]
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$\hat e$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 $\frac{1}{2}$]
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