0
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0answers
96 views

A question in Chapter III.4 of Dino Lorenzini's “An Invitation to Arithmetic Geometry”

Question 1 I am studying in the book "An Invitation to Arithmetic Geometry" by Prof. Dino Lorenzini. In Chapter III Section 4, we consider the following condition: Let $A$ be a Dedekind domain ...
9
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1answer
177 views

Primes of ramification index 1 with inseparable residue field extension

I've been reading through Neukirch's Algebraic Number Theory, and I'm a little puzzled about a possibility with ramification of primes. As usual, let $\mathcal{O}_K$ be a Dedekind domain with field ...
12
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0answers
177 views

What is Spec of the Adeles?

Let $K$ be a global field and $A_K$ the ring of adeles. What are the prime ideals of $A_K$? I have been told that a full proof of this is quite subtle, but have been unable to find a reference ...
4
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0answers
94 views

Curve - non singular curve and its genus

Help me please with this problem:$ X \subset \mathbb{P}^{2}$ defined as $x^{3}y+y^{3}z+z^{3}x=0$ 1.Prove X - non singular curve and find its genus. 2.Prove X - maximal curve over $F_{8}$ field, and ...
4
votes
1answer
151 views

$\pi^{tame}(\mathbb{A}^1_k)$ is trivial

Fixed an algebraically closed field of characteristic $p>0$, it is well known the result of the title: $\pi^{tame}(\mathbb{A}^1_k)\simeq 1$. Where the tame fundamental group, in this situation, ...