Quasi-finite morphismIn algebraic geometry, a branch of mathematics, a morphism f : X → Y of schemes is quasi-finite if it is of finite type and satisfies any of the following equivalent conditions: Every point x of X is isolated in its fiber f−1(f(x)). In other words, every fiber is a discrete (hence finite) set. For every point x of X, the scheme f−1(f(x)) = X ×YSpec κ(f(x)) is a finite κ(f(x)) scheme. (Here κ(p) is the residue field at a point p.) For every point x of X, is finitely generated over .
Étale morphismIn algebraic geometry, an étale morphism (etal) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology.
Flat morphismIn mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., is a flat map for all P in X. A map of rings is called flat if it is a homomorphism that makes B a flat A-module. A morphism of schemes is called faithfully flat if it is both surjective and flat. Two basic intuitions regarding flat morphisms are: flatness is a generic property; and the failure of flatness occurs on the jumping set of the morphism.
Morphism of schemesIn algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. It is, by definition, a morphism in the category of schemes. A morphism of algebraic stacks generalizes a morphism of schemes. By definition, a morphism of schemes is just a morphism of locally ringed spaces. A scheme, by definition, has open affine charts and thus a morphism of schemes can also be described in terms of such charts (compare the definition of morphism of varieties).
Spirit (rover)Spirit, also known as MER-A (Mars Exploration Rover – A) or MER-2, is a Mars robotic rover, active from 2004 to 2010. Spirit was operational on Mars for sols or 3.3 Martian years ( days; ). It was one of two rovers of NASA's Mars Exploration Rover Mission managed by the Jet Propulsion Laboratory (JPL). Spirit landed successfully within the impact crater Gusev on Mars at 04:35 Ground UTC on January 4, 2004, three weeks before its twin, Opportunity (MER-B), which landed on the other side of the planet.
