Algebraic Geometry 3, Winter term 2023/24.
Lecture course notes.

Content

Bibliography


AK

A. Altman, S. Kleiman, Introduction to Grothendieck Duality, Springer Lecture Notes in Math. 146 (1970).

AM

M. Atiyah, I. Macdonald, Introduction to Commutative Algebra, Addison-Wesley

B

A. Borel, Linear algebraic groups, Springer.

BH

W. Bruns, J. Herzog, Cohen-Macaulay Rings, revised ed., Cambridge Univ. Press (1998).

BK

M. Brion, S. Kumar, Frobenius splitting methods in geometry and representation theory, Birkhäuser Progr. in Math. 2007.

Bo

S. Bosch, Algebraic Geometry and Commutative Algebra, Springer Universitext 2013

BouA

N. Bourbaki, Algèbre, or in English: Algebra, Ch. 1–10.

BouAC

N. Bourbaki, Algèbre commutative, or in English: Commutative Algebra, Ch. 1–10.

EGA

J. Dieudonné, A. Grothendieck, Éléments de géométrie algébrique, Springer (1971)/Publ. Math.IHÉS 4 (1960), 8 (1961), 11 (1961), 17(1963), 20 (1964), 24(1965), 28 (1966), 32 (1967). See https://www.numdam.org/.

ALG2

U. Görtz, Kommutative Algebra, SS23, https://math.ug/a2-ss23/, 2023.

GW1

U. Görtz, T. Wedhorn, Algebraic Geometry I, 2nd ed., Springer 2010.

GW2

U. Görtz, T. Wedhorn, Algebraic Geometry II, Springer 2023.

Gr

A. Grothendieck, Sur quelques points d’algèbre homologique, Tohoku Math. J. 9 (1957), 119–221.

H

R. Hartshorne, Algebraic Geometry, Springer Grad. Texts in Math. 52, corr. 8th printing (1997)

Kl

S. Kleiman, Relative duality for quasi-coherent sheaves, Comp. Math. 41, no. 1 (1980), 39–60.

M2

H. Matsumura, Commutative Ring Theory, Cambridge University Press

Mi

J. Milne, Algebraic groups, Cambridge Univ. Press 2017.

Mu

D. Mumford, Abelian varieties, Oxford University Press 1970.

Ra

A. Ramanathan, Schubert varieties are arithmetically Cohen-Macaulay, Invent. math. 80 (1985), 283–294.

Stacks

Stacks Project Authors, Stacks Project, stacks.math.columbia.edu (2023).

We

C. Weibel, An introduction to homological algebra, Cambridge studies in adv. math. 38, Cambridge Univ. Press 1994.

Va

R. Vakil, The rising sea. Foundations of algebraic geometry,
https://math.stanford.edu/~vakil/216blog/FOAGnov1817public.pdf