If $X$ is a scheme, $\mathcal{F}$ is a quasi-coherent sheaf and $L$ is an ample line bundle, why it holds $H^0(X, \mathcal{F} \otimes L^n) = Hom(L^{-n}, \mathcal{F})$?
2026-03-25 05:05:40.1774415140
Hom, H$^n$ and tensor product
74 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in SHEAF-COHOMOLOGY
- Question about notation for Čech cohomology and direct image of sheaves in Hartshorne
- Image of a morphism of chain complexes of sheaves via direct/inverse image functor
- Does $H^2(X_{Zar},\mathcal{O}_X^\times)=0$ for $X$ a regular scheme?
- Computing the dimension of $H^0(X, \mathcal{O}_X(D))$, where $D \subset X$ is a divisor
- Is the cohomology of a stalk the same as the stalk of the cohomology sheaf?
- If $H^i(\tilde{X}, \mathcal{F}) = 0$, then is it true that $H^i(X, \mathcal{F}) = 0$?
- Conditions on $\mathcal{F}$ such that $\chi(\mathcal{F}) = 0$ for a coherent sheaf on a curve over $k$.
- Cohomology and inverse image of divisors
- $\dim H^0(X, \mathcal{O}_D) \leq 1 + \deg D$ when $-1 \leq \deg D \leq g - 1$
- Bott vanishing from the Euler sequence
Related Questions in DERIVED-FUNCTORS
- Derived functors in the category of sheaves
- Question about $\mbox{Ext}$ groups in abelian categories
- Determining right derived functor of the left exact functor $M \to M[p]$.
- Defining contravariant left/right-exact functor with opposite category?
- Transfer modules and Weyl algebra
- Derived functors and induced functors
- Tor functor on a torsion ring
- Properties of derived functors
- Cohomology of $Hom$'s between Complexes
- When does the inverse image functor commute with internal hom?
Related Questions in DERIVED-CATEGORIES
- $A$ - dga over field, then $H^i(A) = 0, i > 1$ implies $HH_i(A) = 0, i < -1$
- Images of derived categories of $X, Z$ in derived category of blow up
- derived category of quotient category
- Are quasi-isomorphisms always invertible in the homotopy category?
- Derived functors and induced functors
- Distinguished triangle induced by short exact sequence
- When does the inverse image functor commute with internal hom?
- Derived functor defined with an adapted subcategory
- Ext functor in derived categories
- Serre duality in derived category
Related Questions in HOM-FUNCTOR
- When can functors fail to be adjoints if their hom sets are bijective?
- Existence of morphisms in a free completion under directed colimits,$\lambda$-accessible category
- Preservation of limits by representable functors
- There is a natural morphism $\lim\limits_{\longleftarrow} \beta \to \lim\limits_{\longleftarrow} \beta \circ \varphi^{op}$?
- Fully faithful nerve ⟹ injective on objects?
- $\operatorname{Hom}$ functor is projective?
- Nearly locally presentable categories
- Existence of injective homomorphism
- Isomorphism between Hom-space and $k$
- Is “monoidal category enriched over itself” the same as “closed monoidal category”?
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?