Let $G$ be finite group scheme over a field $k$. What are some examples of $G$ such that it is not affine?
2026-02-22 23:10:57.1771801857
Examples of finite group schemes over a field which are not affine
193 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GROUP-THEORY
- What is the intersection of the vertices of a face of a simplicial complex?
- Group with order $pq$ has subgroups of order $p$ and $q$
- How to construct a group whose "size" grows between polynomially and exponentially.
- Conjugacy class formula
- $G$ abelian when $Z(G)$ is a proper subset of $G$?
- A group of order 189 is not simple
- Minimal dimension needed for linearization of group action
- For a $G$ a finite subgroup of $\mathbb{GL}_2(\mathbb{R})$ of rank $3$, show that $f^2 = \textrm{Id}$ for all $f \in G$
- subgroups that contain a normal subgroup is also normal
- Could anyone give an **example** that a problem that can be solved by creating a new group?
Related Questions in COMMUTATIVE-ALGEBRA
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Extending a linear action to monomials of higher degree
- Tensor product commutes with infinite products
- Example of simple modules
- Describe explicitly a minimal free resolution
- Ideals of $k[[x,y]]$
- $k[[x,y]]/I$ is a Gorenstein ring implies that $I$ is generated by 2 elements
- There is no ring map $\mathbb C[x] \to \mathbb C[x]$ swapping the prime ideals $(x-1)$ and $(x)$
- Inclusions in tensor products
- Principal Ideal Ring which is not Integral
Related Questions in SCHEMES
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- Do torsion-free $\mathcal{O}_X$-modules on curves have dimension one?
- $\mathbb{C}[x,y]$ is the sections of Spec $\mathbb{C}[x,y]$ minus the origin?
- Finitely generated $k-$algebras of regular functions on an algebraic variety
- Is every open affine subscheme of an algebraic $k-$variety an affine $k-$variety?
- Scheme Theoretic Image (Hartshorne Ex.II.3.11.d)
- Is this a closed embedding of schemes?
- Adjunction isomorphism in algebraic geometry
- Closed connected subset of $\mathbb{P}_k^1$
- Why can't closed subschemes be defined in an easier way?
Related Questions in GROUP-SCHEMES
- Examples of finite group schemes over a field which are not affine
- Every profinite group is naturally an affine group scheme over $\mathbb Q$?
- stabilizer of action of a group scheme on a scheme
- What is difference between constant group scheme associated with cyclic group and $\mu_n$
- Equivalence definition of affine (group) schemes
- Notion of inner automorphisms for group schemes
- Subgroup scheme of a constant group scheme
- free action of group scheme
- How can an elliptic curve be regarded as a group scheme?
- Constructing a group scheme associated to a coherent module.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
It is immediate from the definition that any finite group scheme (indeed, any finite scheme) over a field is affine. If a morphism is finite, that means there is an open cover of the base by affine sets whose inverse images are affine and for which the morphism comes from a finite map of rings. When the base is Spec of a field, this just means the domain scheme itself must be affine (and Spec of a finite-dimensional algebra over the field). More generally, any finite morphism is affine, so if the codomain is affine then so is the domain.