Is there a conjecture/result about the number of rational solutions of curves with genus ≥ 2 over the algebraic closure of Q? Is this set thought to be also finite as in Faltings's theorem over number fields?
2026-03-26 13:52:17.1774533137
Mordell's conjecture for curves over the field of algebraic numbers
70 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related 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 ALGEBRAIC-CURVES
- Singular points of a curve
- Finding a quartic with some prescribed multiplicities
- Tangent lines of a projective curve
- Value of $t$ for which a curve has singular points.
- Reference for $L$-functions of curves
- Bézout's theorem for intersection of curves
- Curves of genus 0
- Multiplicity of singular points in a curve.
- Intersection of a quartic and conics.
- Rational points on conics over fields of dimension 1
Related Questions in ARITHMETIC-GEOMETRY
- Showing that a Severi-Brauer Variety with a point is trivial
- Definition of scheme defined over a ring A
- Galois representation on Tate module of a twist of an elliptic curve
- What is the difference between algebraic number theory, arithmetic geometry and diophantine geometry?
- Questions about Zeta Function of Singular Plane Curve
- Brauer group of global fields
- Structure of étale maps
- Unipotent Groups and Torsors
- why is multiplication by n surjective on an abelian variety
- Poincare duality compatible with the definition of compactly supported cohomology in etale cohomology?
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?