# Tagged Questions

**13**

votes

**6**answers

1k views

### Text for Algebraic Number Theory

I have the privilege of teaching an algebraic number theory course next fall, a rare treat for an algebraic topologist, and have been pondering the choice of text. The students will know some ...

**5**

votes

**1**answer

1k views

### Motivation for the proof of Hilbert's Theorem 90

The proof of Hilbert's Theorem 90 about cyclic extensions goes like this: Let $\sigma$ be the generator of the Galois group of order $n$ and let $b$ have norm $1$, i.e. $b \sigma(b) \cdots ...

**3**

votes

**2**answers

458 views

### Local methods in algebraic number theory

I'm currently reading about local and global fields in number theory. I have trouble seeing the point or exactly how they help answer questions about e.g. number fields. To be more specific:
What ...

**1**

vote

**1**answer

702 views

### Good Minkowski Theory and Commutative Algebra Books

I am not so familiar with the theory of measures which Andre Weil uses to develope the Class Field Theory.
However, I am interested in learning algebraic number theory and I recently found that the ...

**5**

votes

**1**answer

546 views

### Why are absolute values more natural than discrete valuations?

It is true that considering the archimedean places as well is more general, but that still doesn't explain why it is more natural. If we consider both the definitions of an absolute value and that of ...

**6**

votes

**1**answer

444 views

### Can algebraic number fields be generalized in a similar way to function fields in 1 variable over a finite field?

Global fields consist of finite extensions of $\mathbb{Q}$ (algebraic number fields) and finite extensions of $\mathbb{F}_q(x)$ (function fields in 1 variable over a finite field). The latter are ...