In section 3(Page 50) of this paper, it is mentioned that the Kummer map, $\hat{E}(\mathfrak{m}_n)\rightarrow H^{1}(k_n,T)$ along with the Weil pairing induces a cup product of Galois cohomology groups. How is the Kummer map defined? I know that $\hat{E}(\mathfrak{m}_n)$ injects into $E(k_n)$ and then somehow the Kummer sequence for elliptic curves is involved to get a map to $H^{1}(k_n,T)$? Can someone help?
2026-03-25 03:02:08.1774407728
Kummer map on the formal group of elliptic curve
83 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in ELLIPTIC-CURVES
- Can we find $n$ Pythagorean triples with a common leg for any $n$?
- Solution of $X^5=5 Y (Y+1)+1$ in integers.
- Why does birational equivalence preserve group law in elliptic curves?
- CM elliptic curves and isogeny
- Elliptic Curve and Differential Form Determine Weierstrass Equation
- Difficulty understanding Hartshorne Theorem IV.4.11
- Elementary Elliptic Curves
- Flex points are invariant under isomorphism
- The Mordell equation $x^2 + 11 = y^3$.
- How do we know that reducing $E/K$ commutes with the addition law for $K$ local field
Related Questions in GALOIS-COHOMOLOGY
- Square classes of a real closed field
- Surjectivity of the inv map in Global class field theory
- $H^1(G, \mathbb{Z}/p \mathbb{Z})$ and linearly independent elements in open subgroups.
- First cohomology group of the $n$-torsion of an elliptic curve
- Surjectivity of map of étale sheaves
- Hilbert 90 and K-forms
- How can a point on an elliptic curve be considered a galois cohomology class?
- Tate Cohomology of Squares
- Galois extension of exponent $mp^r$ in characteristic $p$
- What should one know before learning galois cohomology
Related Questions in KUMMER-THEORY
- kummer extension: converse part
- Kummer-type transformation for a special 2F2 hypergeometric function
- Show that this Galois group is solvable (Base case)
- Galois extension of exponent $mp^r$ in characteristic $p$
- Special case of normal basis theorem - Artin 16.M.13
- Kummer Theory Proof
- Kummer Theory Square Extension
- Cyclic Field Extension of Local Field
- Kummer Generators for Cyclic Extensions
- Why p-cyclic extension iff $p^m$-cyclic extension $\forall m$
Related Questions in FORMAL-GROUPS
- What is the classification of 1-dimensional commutative formal group laws over $\mathbb{Z}$ up to isomorphism?
- Is $\Bbb Z[x_1,x_2,\Bbb…]/(x_ix_j- {i+j \choose i}x_{i+j})$ a noetherian ring?
- Is $ \frac{x+y}{x^3 y^3 - x^3 y - x y^3 + 2 xy + 1} $ a formal group law?
- Formal group law and Koenigs function conjecture !?
- Height of a formal group law homomorphism
- The formal group law of height $ \ 2$ or $ \ 3 $ over $\mathbb{F}_p$
- Definition of an invariant differential form on a formal group
- Why do we say always "$1$-dimensional formal group law"?
- Showing the center of an endomorphism ring is a direct summand
- Are formal groups associated to various groups different?
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?