# Tagged Questions

**3**

votes

**3**answers

489 views

### Non existence of cyclic infinite linear algebraic groups

Let $G$ be a linear algebraic group defined over some algebraically closed field $\mathbb{K}$ and also over some subfield $k\subset \mathbb{K}$. There is thus a natural group structure on the set of ...

**1**

vote

**1**answer

137 views

### Compatibility of two definitions of elliptic elements in GLn

For an element $g$ of a connected reductive group $G$ (over a local field),
$g$ is called $elliptic$ if it is semisimple and the maximal split subtorus of the center of the centralizer of $g$ is ...

**2**

votes

**0**answers

44 views

### on degree zero elements in adelic groups

Let $G$ a split connected reductive group and $G(\mathbb{A})$ his points in the ring of adeles.
We have a degree map $G(\mathbb{A})\rightarrow X_{*}(Z)$ where $Z$ is the center of $G$.
Let ...

**5**

votes

**0**answers

141 views

### On Langlands Pairing and transfer factors

In the paper "On the definition of transfer factors" Langlands and Shelstad define a certain number of factors $\Delta_{I}$, $\Delta_{II}$,$\Delta_{III,1}$,$\Delta_{III,2}$, which are roots of unity.
...

**2**

votes

**1**answer

247 views

### finiteness of class number: a bound for semi-simple groups?

Let $F$ be a number field, and $G$ a connected semi-simple linear algebraic $F$-group, which does not contain anisotropic (simple) $F$-factors. Write $\hat{F}$ for the ring of finite adeles ...

**1**

vote

**1**answer

298 views

### Centralizer of elliptic elements in $GL(2)$

Consider a global field $F$ and the group $\Gamma =GL(2,F)$. An element $\gamma \in \Gamma$ is called elliptic, if its eigenvalues do not lie in $F$. Now consider a completion $F_v$ of $F$ and $G_v = ...

**3**

votes

**0**answers

271 views

### idelic closures of units of number fields

Let $K$ be a number field, $\mathcal O _K^\times$ its group of integral units and $\mathcal O _{K,+} ^\times$ its group of totally positive units. Denote further by $\widehat{\mathcal O }_K^\times$ ...

**7**

votes

**1**answer

754 views

### Parametrization of 2-dimensional torus

The units with norm $+1$ in a pure cubic number field $K$ generated
by a cube root of $m = ab^2$, where $a$ and $b$ are coprime and
squarefree integers, correspond to integral points on the torus
$$ ...