Department Mathematik
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Algebraic Geometry 1, chapter 2 and 3 :

Lecture 10 (part 1) (1,5 Gb, 45mn), Lecture 10 (part 2) (1,6 Gb, 49mn) :
The Zariski topology on Spec(A). Presheaves on a topological space (3 December)
Lecture 11 (part 1) (1,6 Gb, 50mn), Lecture 11 (part 2) (1,4 Gb, 44mn) :
Presheaves and sheaves on a topological space; examples (8 December)
Lecture 12 (part 1) (1,6 Gb, 50mn), Lecture 12 (part 2) (1,4 Gb, 43mn) :
Stalks of presheaves. Characterisation of sheaves isomorphisms with stalks (10 December)
Lecture 13 (part 1) (1,2 Gb, 36mn), Lecture 13 (part 2) (2 Gb, 101mn) :
Sheafification. The structure sheaf on Spec(A) (15 December)
Lecture 14 (part 1) (1,2 Gb, 38mn), Lecture 14 (part 2) (1,7 Gb, 54mn) :
The isomorphism A = O_{Spec(A)}(Spec(A)). Commutative ringed spaces, morphisms. Schemes (12 January)
Lecture 15 (part 1) (1,3 Gb, 44mn), Lecture 15 (part 2) (1,5 Gb, 50mn) :
Morphisms of schemes, morphisms to an affine scheme. Open subschemes (14 January)
Lecture 16 (part 1) (1,6 Gb, 53mn), Lecture 16 (part 2) (1,3 Gb, 43mn) :
Morphisms to affines shemes (end); examples. $S$-schemes. Morphisms locally of finite type, morphisms of finite type (19 January)
Lecture 17 (part 1) (280 Mb, 10mn), Lecture 17 (part 2) (1,3 Gb, 45mn), Lecture 17 (part 3)(1 Gb, 34mn) :
(locally of) finite type morphisms (end), affine and finite morphisms, open immersions, closed immersions (21 January)
Lecture 18 (part 1) (1,4 Gb, 47mn), Lecture 18 (part 2) (1,6 Gb, 54mn):
Absolute properties of schemes: irreducible, reduced, integral, quasi-compact, noetherian. Gluing datas and gluing condition (26 January)
Lecture 19 (part 1) (1,4 Gb, 45mn), Lecture 19 (part 2) (1,4 Gb, 48mn):
Gluing datas and gluing condition: proofs. Examples. Existence of fiber products (28 January)
Lecture 20 (part 1) (1,3 Gb, 44mn), Lecture 20 (part 2) (1,6 Gb, 52mn):
Construction of fiber products of schemes. Examples (2 February)
Lecture 21 (part 1) (1,3 Gb, 44mn), Lecture 21 (part 2) (1,6 Gb, 53mn):
Examples of fiber products of schemes; fibers, base change. Closed immersions (4 February)
Lecture 22 (part 1) (1,3 Gb, 45mn), Lecture 22 (part 2) (1,6 Gb, 53mn):
Characterisation of closed immersions. Factorisation of a finite morphism as a closed immersion followed by a finite surjective morphism (9 February)
Lecture 23 (part 1) (1,1 Gb, 38mn), Lecture 23 (part 2) (1,8 Gb, 62mn), Lecture 23 (part 3) (640 Mb, 21mn):
Dimension in finite morphisms. Finite morphisms are proper. Quotient by the action of a finite group. n-th symmetric product of A^1 = A^n , n-th symmetric product of P^1 = P^n (End of the lecture). (11 February)