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Results tagged with algebraic-number-theory
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user 105625
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
Accepted
Artin map restricted to base field
I've finally found the answer to my question by perusing Serre's Local Fields, Ch.XIII, specifically Propositions 10-12, which contain the functorial properties of the Artin symbol used below.
We des …
- 636
5
votes
1
answer
421
views
Artin map restricted to base field
Let $M/L/K$ be a tower of local fields such that $M/L$ is abelian with Galois group $G$. The Artin map $\psi_{M/L}$ restricted to $K^\times$ is a continuous map to $G$ and thus corresponds to some abe …
- 636
1
vote
Accepted
Relation in Brauer group coming from trace form
$\newcommand{\tr}{\operatorname{tr}}\newcommand{\Ell}{\operatorname{Ell}}$That was quicker to solve than I expected.
Consider the trace map
$$
\tr : GW(L) \to GW(K)
$$
between the Grothendieck-Witt ri …
- 636
5
votes
1
answer
252
views
Relation in Brauer group coming from trace form
Let $L/K$ be a cubic (or, more generally, odd-order) extension of fields of characteristic $0$. To every element $a \in L^\times$ we can associate the quadratic form
\begin{align*}
q_a : L &\to K \\
x …
- 636