# Questions tagged [algebraic-number-theory]

Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

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### Central division algebras over $ \mathbb{Q} $

**4**

**1**answer

### Torsion points on $E/\mathbb{Q}$ with large coordinates

**2**

**1**answer

### How to compute the intersection of an ideal with the maximal order of a subfield?

**9**

**1**answer

### Absolute values of non-unit algebraic integers at all infinite places

**4**

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### Is every Dedekind domain the integral closure of some principal ideal domain?

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### Reducibility of a cubic over a number field

**2**

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### Construction of genus class fields

**4**

**4**answers

### The integral closure $\overline{\mathbb{Z}}$ and the group $\overline{\mathbb{Z}}^{\times}$

**3**

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### Norm groups of number fields

**3**

**1**answer

### Centralizer of the absolute Galois group of a number field

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### For any $n-1$ elements of $\mathbb Z/n\mathbb Z$, we can make $0$ using $\{-,+,\times\}$ without parentheses

**5**

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### Explicit computations of the fundamental groups of perfectoid spaces

**4**

**1**answer

### is every positive real cyclotomic number the norm of a cyclotomic?

**3**

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### A question on the Bombieri-Lang conjecture

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### Topologically finitely generated absolute Galois group is topologically finitely presented

**2**

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### Topologically finitely generated non-abelian isomorphic absolute Galois groups

**4**

**1**answer

### Non-abelian isomorphic absolute Galois groups of fields of different characteristic

**5**

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### Goldfeld resolution of the quadratic class number problem

**4**

**1**answer

### Can every square root be represented as a linear combination on roots of unity? [duplicate]

**2**

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### Reference Request - New proof of Ribet's level lowering by Khare and Wintenberger

**2**

**2**answers

### Galois stable elements of the Picard group of a curve and the rational divisors

**0**

**1**answer

### Solving the inequality between a and b [closed]

**6**

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### Rational point oracle for smooth projective varieties

**1**

**1**answer

### Elliptic curve over $\mathbb{Q}(T)$ receiving only constant maps from modular curves

**3**

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### Are class numbers of number fields with prime degree often $1$?

**5**

**1**answer

### Explicit construction of division algebras of degree 3 over $\mathbb{Q}$

**5**

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### Maximum value of newform from Galois representation

**1**

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### Powers of automorphic Eisenstein series

**9**

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### Commutative algebra details on patching when proving $R = \mathbb{T}$ theorem (Calegari-Geraghty Paper)

**4**

**1**answer

### Computing the genus of certain ternary indefinite lattices

**3**

**2**answers

### Dedekind Zeta functions of Biquadratic fields

**2**

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### Weierstrass points in Artin-Schreier extensions of the rational function field in characteristic $p$

**2**

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### Has there been much research on the Iwasawa theory of bi-quadratic fields?

**16**

**1**answer

### Principal ideal domains with finitely many units

**6**

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### Galois cohomology with coefficients in the unit group of a cyclotomic field

**2**

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### Hard “one-dimensional” cases of Fermat's Last Theorem

**3**

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### Why are critical points important for dynamical systems?

**3**

**1**answer

### Absolute Galois group with unique closed non-open subgroup

**0**

**1**answer

### Faithful irreducible representations of the dihedral group $D_{2p}$, of dimension at most $p-1$

**1**

**1**answer

### “Violent” field isomorphisms and $p$-adic “degrees” of complex numbers

**3**

**1**answer

### Connecting different ways of constructing cubic extensions of $\mathbb{Q}$

**1**

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### $\frac{1}{\pi} \int_{0}^\infty \frac{\log|\left(\frac{1}{2}+it\right)\zeta\left(\frac{1}{2}+it\right)|}{\frac{1}{4}+t^2}dt $

**5**

**2**answers

### Why are these sets divisible by n?

**31**

**6**answers

### Using algebraic geometry to understand class field theory

**22**

**1**answer

### Why is the regulator of the degree 11 extension of $\mathbb{Q}$ so large?

**2**

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### Generalizations of Artin–Verdier duality?

**10**

**1**answer

### How Dirichlet proved Dirichlet's unit theorem for general number fields?

**5**

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### Truncation and weighted orbital integrals in hyperbolic term of trace formula for $\mathrm{GL}(2)$

**1**

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### What conditions on primes makes it non principal?

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