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Results tagged with algebraic-number-theory
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user 450
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
2
votes
Localizations as free, finite rank modules
Dear Pedro, actually the localization $O_p$ is always free of rank $n$ over
$\mathbb Z_{(p)}$, independently of the number of primes above $p$.The reason is that
a) $O_p$ is of finite type and tors …
- 47.5k
4
votes
Accepted
Are all Finite Subsets of Affine n-space Algebraic sets, and related question
Let $I\subset \mathbb Q[x_1,...,x_n]$ be the ideal generated by the polynomials $P_1,...,P_k$ and $A$ the $\mathbb Q$-algebra $A=\mathbb Q[x_1,...,x_n]/I$.
You are interested in the scheme $V=Spec(A …
- 47.5k
30
votes
Is there a Riemann-Roch for smooth projective curves over an arbitrary field?
Dear Hugo, the wonderful formalism of schemes allows us to have a Riemann-Roch theorem for a projective curve $X$ over an arbitrary field $k$, even without any assumption of smoothness.
It says, like …
- 47.5k
2
votes
Etale coverings of certain open subschemes in Spec O_K
Here is a result concerning Riemann surfaces which might be relevant (cf. your EDIT).
Fix a Riemann surface $X$, a discrete closed subset $D\subset X$ and put $X_0 =X\setminus D$ . Let $\mathcal RevR …
- 47.5k