By Lei Fu
Etale cohomology is a vital department in mathematics geometry. This e-book covers the most fabrics in SGA 1, SGA four, SGA four half and SGA five on etale cohomology conception, together with respectable thought, etale primary teams, Galois cohomology, etale cohomology, derived different types, base switch theorems, duality, and l-adic cohomology. the necessities for examining this ebook are uncomplicated algebraic geometry and complex commutative algebra.
Read Online or Download Etale Cohomology Theory PDF
Best algebraic geometry books
The amount is predicated on a direction, "Geometric versions for Noncommutative Algebras" taught by means of Professor Weinstein at Berkeley. Noncommutative geometry is the learn of noncommutative algebras as though they have been algebras of services on areas, for instance, the commutative algebras linked to affine algebraic types, differentiable manifolds, topological areas, and degree areas.
This quantity includes the Lecture Notes of the CIMPA/TUBITAK summer time college preparations, neighborhood platforms and Singularities held at Galatasaray collage, Istanbul in the course of June 2007. the quantity is meant for a wide viewers in natural arithmetic, together with researchers and graduate scholars operating in algebraic geometry, singularity idea, topology and similar fields.
This ebook presents a self-contained exposition of the speculation of algebraic curves with no requiring any of the must haves of contemporary algebraic geometry. The self-contained therapy makes this significant and mathematically crucial topic available to non-specialists. while, experts within the box could be to find numerous strange subject matters.
Das vorliegende Buch beruht auf Vorlesungen und Seminaren für Studenten mittlerer und höherer Semester im Anschluß an eine Einführung in die komplexe Funktionentheorie. Die Theorie Riemannscher Flächen wird als ein Mikrokosmos der Reinen Mathematik dargestellt, in dem Methoden der Topologie und Geometrie, der komplexen und reellen research sowie der Algebra zusammenwirken, um die reichhaltige Struktur dieser Flächen aufzuklären und an vielen Beispielen und Bildern zu erläutern, die in der historischen Entwicklung eine Rolle spielten.
- Notes on finite group theory [Lecture notes]
- The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry
- Measure, Topology, and Fractal Geometry
- A geometric introduction to K-theory [Lecture notes]
Additional info for Etale Cohomology Theory
It follows that fg(s ) is also a local homomorphism. Hence f is a morphism of schemes. 2. Let g : S → S be a quasi-compact faithfully flat morphism, and let S = S ×S S . For any scheme Z, the sequence Hom(S, Z) → Hom(S , Z) ⇒ Hom(S , Z) is exact. Proof. 1. 3. Let g : S → S be a quasi-compact faithfully flat morphism, S = S ×S S , X and Y two S-schemes, X = X ×S S , Y = Y ×S S , X = X ×S S , and Y = Y ×S S . Then the sequence HomS (X, Y ) → HomS (X , Y ) ⇒ HomS (X , Y ) is exact. Proof. 2, the sequences Hom(X, Y ) → Hom(X , Y ) ⇒ Hom(X , Y ) Hom(X, S) → Hom(X , S) ⇒ Hom(X , S) are exact.
I) Let B0 be an A0 -algebra, Bλ = B0 ⊗A0 Aλ , B = B0 ⊗A0 A, (Cλ ) a direct system of A0 -algebras such that we have a morphism of direct systems from (Aλ ) to (Cλ ), and C = limλ Cλ . If B0 is an A0 -algebra of finite type −→ (resp. finite presentation), then the canonical map lim HomAλ (Bλ , Cλ ) → HomA (B, C) −→ λ is injective (resp. bijective). (ii) For any A-algebra B with finite presentation, there exists an Aλ algebra Bλ with finite presentation for a sufficiently large λ such that B ∼ = Bλ ⊗Aλ A.
7. Assume g : Y → Y is a quasi-compact faithfully flat morphism. Then the topology on Y coincides with the quotient topology induced from Y . 8. Let g : S → S be a quasi-compact faithfully flat morphism, S = S ×S S , O(S) (resp. O(S ), resp. O(S )) the set of open subsets of S (resp. S , resp. S ), and F(S) (resp. F(S ), resp. F(S )) the January 5, 2011 11:3 World Scientific Book - 9in x 6in 34 Etale Cohomology Theory set of closed subsets of S (resp. S , resp. S ). Then the following sequences are exact: p−1 1 O(S) → O(S ) ⇒ O(S ), p−1 2 p−1 1 F(S) → F(S ) ⇒ F(S ).