Suppose $X$ is an abelian variety over a field $k$. Consider the de Rham cohomology of $X^{\vee}$ (denoted by $H_{dR}^i(X^{\vee})$). I want to ask is $H_{dR}^i(X^{\vee})$ naturally dual to $H_{dR}^i(X)$?
2026-03-25 16:03:39.1774454619
de Rham cohomology of dual abelian variety
56 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 DE-RHAM-COHOMOLOGY
- DeRham Cohomology of punctured plane and homotopy.
- Chern-Weil homomorphism and Chern/Pontryagin/Euler class
- Finite dimensionality of the "deRham cohomology" defined using $C^{k,\alpha}$ forms instead of smooth forms.
- Averaging of a differential form.
- De Rham cohomology groups of projective real space
- Homotopy invariance of de Rham cohomology
- The Converse of Poincare Lemma
- How does one introduce characteristic classes
- There is no smooth diffeomorphism $f:\mathbb R^3 \setminus [-\frac{1}{2}, \frac{1}{2}]^3 \to \mathbb R^3$
- Why $H_{dR}^1(M) \simeq \mathbb R^n$ when $H_1(M,\mathbb Z)$ has $n$ generators?
Related Questions in ABELIAN-VARIETIES
- Relative Abelian Varieties
- why is multiplication by n surjective on an abelian variety
- Commutativity of Abelian schemes
- Morphism from complete variety to an affine variety
- What are applications of etale cohomology and Abelian varieties? (And what is arithmetic geometry?)
- Krull-Schmidt for abelian varieties
- Endomorphism of frobenius scheme
- Is intersection with the power of a polarization injective on the Chow Ring?
- stabilizer of action of a group scheme on a scheme
- Let $E/F$ be a finite field extension of number field $F$. Can one complete integral basis of $F/Q$ to integral basis of $E/Q$?
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?