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Results tagged with algebraic-number-theory
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user 4692
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
15
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4
answers
3k
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Is there much difference between Kronecker's and Dedekind's methods in algebraic number theo...
Edwards, in his book "Divisor theory" says that Kronecker's methods are quite different to Dedekind's and those of today. Is there really much of a difference apart from Kronecker's methods being more …
- 4,351
6
votes
1
answer
631
views
Can algebraic number fields be generalized in a similar way to function fields in 1 variable...
Global fields consist of finite extensions of $\mathbb{Q}$ (algebraic number fields) and finite extensions of $\mathbb{F}_q(x)$ (function fields in 1 variable over a finite field). The latter are isom …
- 4,351
3
votes
2
answers
694
views
What goes wrong in a ring that does not have unique factorization?
Whenever I have seen unique factorization discussed, it is always with respect to the solution of diophantine equations; the equations are solved by splitting the equation into linear functions over a …
- 4,351
0
votes
1
answer
666
views
Hilbert, the nullstellensatz, and algebraic number theory [closed]
I read that Hilbert used the nullstellensatz in algebraic number theory rather than in algebraic geometry. What did he use it for? Today, is the nullstellensatz used in algebraic number theory or othe …
- 4,351