Let $\mathbb{Q}_p$ be the $p$ adic numbers. I am wondering if $\mathbb{Q}_p(p^{2/3})$ an unramified extension or not? Any comments are appreciated!
2026-03-24 23:45:18.1774395918
Is $\mathbb{Q}_p(p^{2/3})$ an unramified extension?
47 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 ALGEBRAIC-NUMBER-THEORY
- Splitting of a prime in a number field
- algebraic integers of $x^4 -10x^2 +1$
- Writing fractions in number fields with coprime numerator and denominator
- Tensor product commutes with infinite products
- Introduction to jacobi modular forms
- Inclusions in tensor products
- Find the degree of the algebraic numbers
- Exercise 15.10 in Cox's Book (first part)
- Direct product and absolut norm
- Splitting of primes in a Galois extension
Related Questions in LOCAL-FIELD
- What is meant by a category of unramified extension of $K$ (a local field)?
- Given a local field is the maximal unramifield extension always finite?
- $(K^*)$ in $K^*$
- How do we know that reducing $E/K$ commutes with the addition law for $K$ local field
- How is $\operatorname{Gal}(K^{nr}/K)$ isomorphic to $\operatorname{Gal}(\bar{k}/k)$?
- Extending a valuation of a local field
- On the Galois group of the maximal $p$-abelian $p$-ramified extension of a number field
- Finite extension of $K$,a finite extension of $\mathbb{Q}_p$, that is Galois?
- Why is $E[2]$ of $E: y^2 = x^3 - p$ over $\mathbb{Q}_p$ ramified?
- Are there any $\mathbb{Q}_p$ which contains the third root of unity?
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?