Suppose we are given an exact sequence
$$ 0\to A\to B\to C\to 0$$
of commutative group scheme over a field $k$. Then does the sequence define an exact sequence of étale sheaves on a $k$-scheme $X$?
I think the question is elementary, but I get confused.
2026-03-26 13:51:27.1774533087
Does an exact sequence of commutative group schemes define an exact sequence of sheaves?
95 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ALGEBRAIC-GEOMETRY
- How to see line bundle on $\mathbb P^1$ intuitively?
- Jacobson radical = nilradical iff every open set of $\text{Spec}A$ contains a closed point.
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- An irreducible $k$-scheme of finite type is "geometrically equidimensional".
- Global section of line bundle of degree 0
- Is there a variant of the implicit function theorem covering a branch of a curve around a singular point?
- Singular points of a curve
- Find Canonical equation of a Hyperbola
- Picard group of a fibration
- Finding a quartic with some prescribed multiplicities
Related Questions in SHEAF-THEORY
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- Question about notation for Čech cohomology and direct image of sheaves in Hartshorne
- Does sheafification preserve surjectivity?
- Image of a morphism of chain complexes of sheaves via direct/inverse image functor
- Tensor of a $k[X]$ module with the structure sheaf of an affine variety is a sheaf
- Sheafy definition for the tangent space at a point on a manifold?
- Whats the relationship between a presheaf and its sheafification?
- First isomorphism theorem of sheaves -- do you need to sheafify if the map is surjective on basis sets?
- An irreducible topological space $X$ admits a constant sheaf iff it is indiscrete.
- Why does a globally generated invertible sheaf admit a global section not vanishing on any irreducible component?
Related Questions in EXACT-SEQUENCE
- Does every sequence of digits occur in one of the primes
- Linear transformation and Exact sequences
- Snake lemma and regular epi mono factorization
- Replacing terms of an exact sequence by quotients
- Module over integral domain, "Rank-nullity theorem", Exact Sequence
- Inclusion and quotient mappings in exact sequences
- Parsing the Bockstein morphism
- Short exact sequence on modules
- G-groups homomorphism regarding the subgroup fixed by G
- A problem about split exact sequences.
Related Questions in ETALE-COHOMOLOGY
- Structure of étale maps
- Clarification about Milne's Etale Cohomology text
- Open normal subgroups of Galois
- Surjectivity of map of étale sheaves
- Twists of etale cohomology
- Explicit formula to compute the conductor of Etale cohomology?
- Long exact sequence in etale cohomology with support
- Cycle class map and generalisation of Kummer theory
- How to compute $H^i_{\operatorname{fppf}}(\mathbb{P}^1,\alpha_p)$?
- Soulé vanishing for $H^2$ of $\mathbb{Q}_p(n)$
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?
- A group scheme whose reduced underlying scheme is not normal
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?