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Results tagged with algebraic-number-theory
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user 10775
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
3
votes
3
answers
3k
views
What (permutation) groups can occur as galois groups of irreducible polynomials of degree n
I think the answers for the first few degrees ($n$) are:
$n=2$, $S_2$
$n=3$, $S_3,A_3$
$n=4$, $S_4,A_4,D_4,\mathbb{Z}_4,K_4$ ($K_4$ is the Klein four group)
$n=5$, $S_5,A_5,D_5,\mathbb{Z}_5,Fr_5$ …
- 805
6
votes
1
answer
635
views
The Jacobian ideal generates the socle of a complete intersection
This is with reference to theorem 5.20 in Vasconcelos book linked (google books) here:
http://tinyurl.com/2967eov
I shall restate the theorem here for easy reference: "If $A=k[[x_1,x_2,...,x_n]]/I$ i …
- 805