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Results tagged with nt.number-theory
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user 1784
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
12
votes
Accepted
A-valued points of projective space
Yes, you (and BCnrd) are absolutely correct and the quoted statement is wrong.
Over any scheme $S$, the $S$-points of $\mathbb P^n$ are the surjections $\mathcal O_S^{\oplus n+1} \to F$ with invertib …
- 13.1k
11
votes
Elliptic Curves over F_1?
As was mentioned by others, currently varieties over $\mathbb F_1$ look uncomfortably like toric varieties or something very close to that. But of course there is a way to think of an elliptic curve a …
- 13.1k
9
votes
4
answers
1k
views
Root systems and sums of squares
It is easy to see that the quadratic form for the root system $A_n$ is a sum of $n+1$ squares of integral linear forms:
$$q_{A_n} = 2 \sum_{i=1}^n x_i^2 - 2 \sum_{i=1}^{n-1} x_i x_{i+1} =
x_1^2 + (x_ …
- 13.1k