2
votes
1answer
84 views

Why do number rings have no endomorphisms

This question is about the analogy between number fields and function fields. It's a soft question and the title misrepresents the question. Consider the projective line over a field. This has many ...
2
votes
1answer
442 views

Who are considered to be masters of arithmetic geometry?

After reading this question I was wondering who are considered to be masters of arithmetic geometry and where can I find the papers which initiated the field arithmetic geometry.
3
votes
0answers
58 views

What applications does the theory of fibered surfaces have

Let $C$ be a smooth projective connected curve over $\mathbf{C}$. Let $X$ be a curve over the function field of $C$. Arakelov and Parshin proved the Mordell conjecture by considering a model for $X$ ...
6
votes
3answers
301 views

Analogies between Prime Ideals and Knots

While reading this question posted at this link: Subjects studied in number theory i interestingly landed up on this Wikipedia page, and was quite amazed to see the variety of branches opening up. ...