Search results
- In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).
en.wikipedia.org/wiki/Scheme_(mathematics)
People also ask
What is a scheme in Algebra?
What is a scheme in physics?
What is an example of a scheme that is not separated?
Which scheme should be called varieties?
Who developed the theory of schemes?
Is an a regular scheme?
2. What are schemes? There are really two parts to a scheme: a topological space, and a thing called the structure sheaf which we think of as functions on the space, all of which is subject to a few conditions regarding compatibility.
In these terms, it seems that we have a single object X (determined by the equation) and we seek to understand X, by computing what happens when we look at the set
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat ...
To take a simple example, consider the a ne plane A2. Over a eld k , the a ne plane can be thought of as having the ring of regular functions k [x; y], where x is the function that assigns a point to its x-coordinate, and y is the function that assigns a point to its y-coordinate.
- 308KB
- 16
10.1 Separated schemes 184 10.2 Properties of separated schemes 186 10.3 Proper morphisms 190 10.4 The valuative criteria* 194 10.5 Exercises 195 11 Schemes of finite type over a field 199 11.1 The formal definition of a variety 199 11.2 Schemes of finite type over a field 200 11.3 Dimension theory for schemes of finite type over a field 201
- 7MB
- 470
Jan 16, 2012 · There are three distinct aspects of schemes that each have their own purpose: (1) Affine schemes generalizing affine varieties by allowing nilpotent elements in the coordinate ring. When you look at families of affine varieties, sometimes the limiting space is only a scheme and not a variety.
The theory of schemes was developed by A. Grothendieck and his school, in an attempt to give an intrinsic description of the objects of algebraic geometry, as opposed to the classical extrinsic description in terms
