Recommended Algebraic Geometry Books for Master’s and Ph.D. Students:
Ahmed Abbes, Éléments de géométrie rigide. Volume I. Construction et étude géométrique des espaces rigides, Birkhäuser/Springer Basel AG, 2010, pages xvi+477.
M.F. Atiyah, I.G. Macdonald, Introduction to Commutative Algebra, Benjamin/Cummings Publishing Co. Inc., 1980, pages x+162.
Vladimir G. Berkovich, Spectral Theory and Analytic Geometry over Non-Archimedean Fields, American Mathematical Society, 1990, pages x+169.
Vladimir G. Berkovich, Étale Cohomology for Non-Archimedean Analytic Spaces, Inst. Hautes Études Sci. Publ. Math. 78 (1993), pages 5-161.
Vladimir G. Berkovich, p-adic Analytic Spaces, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), pages 141-151.
R. Bonnet, Catégorie et α-catégorie des ensembles ordonnés, Publ. Dép. Math. (Lyon) 8.1 (1971), pages 69-90.
N. Bourbaki, Éléments de mathématique. Fasc. XXX, Hermann, Paris, 1964, page 207.
R. Bott, L. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics 82, 2ᵉ éd., Springer-Verlag, 1986, pages xvi+305.
David A. Cox, John Little, Donald O'Shea, Ideals, Varieties, and Algorithms, Springer, 2007, pages xvi+538 (cf. page 6).
Antoine Ducros, Espaces analytiques p-adiques au sens de Berkovich, Astérisque 311 (2007), Séminaire Bourbaki, Exp. No. 958, viii, pages 137-176.
William Fulton, Algebraic Curves: An Introduction to Algebraic Geometry, Addison-Wesley Publishing Company, Redwood City, CA, 1989, pages xxii+226 (cf. page 6).
Kazuhiro Fujiwara, Fumiharu Kato, Foundations of Rigid Geometry I, European Mathematical Society, 2018, pages x+145.
A. Grothendieck, J.A. Dieudonné, Éléments de géométrie algébrique. I., Springer-Verlag, Berlin, 1971, pages ix+466.
Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, 1977, pages xvi+496 (cf. page 6).
J. Harris, Algebraic Geometry: A First Course, Graduate Texts in Mathematics 133, Springer-Verlag, 1992, pages xii+328.
M. Hochster, Prime Ideal Structure in Commutative Rings, Trans. Amer. Math. Soc. 142 (1969), pages 43-60.
Roland Huber, Bewertungsspektrum und rigide Geometrie, Universität Regensburg, Fachbereich Mathematik, 1993, pages xii+309.
Roland Huber, Continuous Valuations, Math. Z. 212.3 (1993), pages 455-477.
Roland Huber, A Generalization of Formal Schemes and Rigid Analytic Varieties, Math. Z. 217.4 (1994), pages 513-551.
Masaki Kashiwara, Pierre Schapira, Categories and Sheaves, Springer-Verlag, Berlin, 2006, pages x+497.
Jean-Louis Krivine, Théorie des ensembles, 2ᵉ édition, Cassini, Paris, 2007, pages 504.
Qing Liu, Algebraic Geometry and Arithmetic Curves, Oxford Science Publications, Oxford University Press, 2002, pages xvi+576 (cf. page 6).
Hideyuki Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1989, pages xvi+320.
J.S. Milne, Étale Cohomology, Princeton University Press, 1980, pages xvi+212.
D. Mumford, Algebraic Geometry I: Complex Projective Varieties, 2ᵉ éd., Classics in Mathematics, Springer-Verlag, Berlin, 1995, pages x+292.
D. Mumford, The Red Book on Varieties and Schemes, Springer-Verlag, 1999, pages xii+213.
M. Nagata, Local Rings, J. Wiley, 1962, pages xii+232.
D. Perrin, Géométrie algébrique : une introduction, Paris : Jouve (CNRS Éditions), 1995, pages 219.
M. Reid, Undergraduate Algebraic Geometry, London Mathematical Society Student Texts 12, Cambridge University Press, Cambridge, 1988, pages x+180.
Peter Scholze, Perfectoid Spaces, Publ. Math. Inst. Hautes Études Sci. 116 (2012), pages 245-313.
I.R. Shafarevich, Basic Algebraic Geometry I, 2ᵉ éd., Springer-Verlag, Berlin, 1994, pages xii+224.
T.A. Springer, Linear Algebraic Groups, 2ᵉ éd., Birkhäuser, 1998, pages x+334.
P. Tauvel, Corps commutatifs et théorie de Galois, Calvage et Mounet, Paris, 2007, pages 318.
C. Weibel, An Introduction to Homological Algebra, Cambridge University Press, 1994, pages x+452.