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245 views

characters on unipotent group

Let $G=GL_{n}$ and $N$ the maximal unipotent subgroup, $\mathbb{A}$ the ring of adeles on a number field $F$. We fix a non trivial character $\psi:F\backslash\mathbb{A}\rightarrow \mathbb{C}^{*}$. …
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2 votes
0 answers
55 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 $G$. …
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1 vote
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140 views

on a decomposition lemma in adelic groups

Let X a curve over an algebraically closed k. Fix $x$ and $y$ two distinct closed points of X. Let G be a connected reductive group over k. We denote Spec $\hat{\mathcal{O}}_{X,x}$ the formal neighbo …
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1 vote
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82 views

decomposition lemma in adelic groups II

Let $X$ a curve on a field $k=\bar{k}$. G a connected reductive group over $k$. Let fix $d$ closed points $(x_{1},...,x_{d})$ of $X$. On each point, we have an évaluation morphisme $ev_{x}:G(k[[t_{x …
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0 votes
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105 views

approximation in Lie algebras

Let $x_{1}$, $x_{2}$, $x_{3}$ three disctinct closed points of a curve $X$ over an algebraically closed field k. Let G a connected reductive group and $\mathfrak{g}$ his Lie algebra. I fix a Borel $ …
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