域$^{1}D_n$上$^{1}D_n$型邻接群的有理等价性

arXiv - MATH - Rings and Algebras Pub Date : 2024-08-28 DOI:arxiv-2408.15528

M. Archita

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摘要

让 $F$ 是$p$-adic 域上的一条光滑几何积分曲线的函数域，其中$p\neq 2.$ 让 $G$ 是定义在 $F$ 上的$^1D_n$型经典邻接群。我们证明$G(F) / R$是微不足道的，其中$R$表示$G(F)$上的{\it rationalequivalence}。

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Rational equivalence on adjoint groups of type $^{1}D_n$ over field $\mathbb{Q}_P(X)$

Let $F$ be the function field of a smooth, geometrically integral curve over a $p$-adic field with $p\neq 2.$ Let $G$ be a classical adjoint group of type $^1D_n$ defined over $F$. We show that $G(F) / R$ is trivial, where $R$ denotes {\it rational equivalence} on $G(F)$.

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arXiv - MATH - Rings and Algebras

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