Tagged Questions
21
votes
3answers
463 views
Why is it “easier” to work with function fields than with algebraic number fields?
I just bought a copy of Jürgen Neukirch's book Algebraic Number Theory. While browsing through it I found a section titled § 14. Function Fields in chapter I. In it the author describes ...
10
votes
2answers
471 views
Why is Hodge more difficult than Tate?
There are strong connections between the Hodge and the Tate conjectures, mainly at the level of similarities and analogies. To quote from an answer of Matthew Emerton on MathOverflow:
"[...] we ...
8
votes
1answer
403 views
What is an intuitive meaning of genus?
I read from the Finnish version of the book "Fermat's last theorem, Unlocking the Secret of an Ancient Mathematical Problem", written by Amir D. Aczel, that genus describes how many handles there are ...
6
votes
2answers
231 views
In what senses are archimedean places infinite?
According to Bjorn Poonen's notes here (ยง2.6), we should add the archimedean places of a number field $K$ to $\operatorname{Spec} \mathscr{O}_K$ in order to get a good analogy with smooth projective ...
3
votes
3answers
204 views
Derived category and so on
I am looking for an introductive reference to the theory of derived categories. Especially I need to start from the very beginning and I need to know how to use this in examples which comes from ...
7
votes
2answers
315 views
How to Compute Genus
How to compute the genus of $ \{X^4+Y^4+Z^4=0\} \cap \{X^3+Y^3+(Z-tW)^3=0\} \subset \mathbb{P}^3$?
We know that the genus of $ \{X^4+Y^4+Z^4=0\} \subset \mathbb{P}^3$ is 3 because the degree is 4.
...
2
votes
1answer
94 views
writing down the minimal discriminant of an elliptic curve
Let $j$ be an integer.
Does there exist an elliptic curve $E_j$ over $\mathbf{Q}$ with $j$-invariant equal to $j$ whose minimal discriminant we can write down in a practical way?
For example, can ...
