Download Algebraic Geometry: A Concise Dictionary by Elena Rubei PDF

By Elena Rubei

Algebraic geometry has a classy, tough language. This e-book features a definition, a number of references and the statements of the most theorems (without proofs) for each of the commonest phrases during this topic. a few phrases of comparable topics are incorporated. It is helping newbies that comprehend a few, yet now not all, easy proof of algebraic geometry to stick with seminars and to learn papers. The dictionary shape makes it effortless and fast to consult.

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We can see easily that it induces homomorphisms from ???????? (????∗ ) to ???????? (????∗ ) for any ????. We say that two morphisms ???? = (???????? ) and ???? = (???????? ) from ????∗ to ????∗ are homotopically equivalent if there are ????-homomorphisms ???????? : ???????? → ????????−1 such that ⋅⋅⋅ ⋅⋅⋅ ????????−2 ????????−2 ???????? − ???????? = ????????+1 ∘ ???????? + ????????−1 ∘ ???????? . ????????−1 ???????? G ???????? G ????????+1 | | | | | | | | || || ???????? −???????? || ???????? || ????????+1 | | | |  ~||   ~|| G ????????−1 G ???????? G ????????+1 ???? ???? G ????????−1 ????−1 ???? ????????+1 ????????+1 G ⋅⋅⋅ G ⋅⋅⋅ . Homotopically equivalent morphisms induce the same homomorphisms in cohomology.

Covering projections. ([33], [91], [112], [158], [184], [215], [234], [247]). Definition. Let ???????? and ???? be two topological spaces. We say that a map ???? : ???????? → ???? is a topological covering projection (covering projection for short) of ???? if, for all ???? ∈ ????, there exists an open subset ???? of ???? such that ????−1 (????) is a disjoint union of open subsets ???????? of ???????? such that ????|???????? : ???????? → ???? is a homeomorphism for all ????. The space ???????? is said to be covering space. Definitions. – We say that a map between two topological spaces, ???? : ???????? → ????, is a local homeomorphism if, for all ???????? ∈ ???????? , there exists an open subset ???? of ???????? containing ???????? such that ????(????) is an open subset of ???? and ???? : ???? → ????(????) is a homeomorphism.

1 : ????????−1 → ???????? ) We call it “homology”, instead of cohomology, if the indices of the ????-modules are decreasing (instead of increasing). A morphism from a complex ????∗ of ????-modules ⋅⋅⋅ ????????−2 ????????−1 G ????????−1 to another complex ????∗ of ????-modules ⋅⋅⋅ ????????−2 ????????−1 G ????????−1 G ???????? G ???????? ???????? G ????????+1 ???????? G ????????+1 ????????+1 ????????+1 G ⋅⋅⋅ G ⋅⋅⋅ is the datum of a sequence of ????-homomorphism ???????? : ???????? → ???????? such that the following diagram commutes ⋅⋅⋅ ⋅⋅⋅ ????????−2 ????????−2 G ????????−1  ????????−1 G ????????−1 ????????−1 ????????−1 G ???????? ????????  G ???????? ???????? ???????? G ????????+1  ????????+1 G ????????+1 ????????+1 ????????+1 G ⋅⋅⋅ G ⋅⋅⋅ .

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