完备离散赋值环上曲线上的不可分解非交叉积Division Algebras
Indecomposable and Noncrossed Product Division Algebras over Curves over Complete Discrete Valuation Rings
摘要：
设T是完备离散赋值环，$\hat{X}$是$S=\spec(T)$上具有闭纤维$X$的光滑射影曲线.用$F$表示$\hat{X}$的函数域，用$\hat{F}$表示$F$关于由闭纤维$X$定义的离散赋值的完备化。本文构造了$F$上的不可分解非交叉积除代数.这是通过定义一个指数保持群同态$s:\br(\hat{F})'\to\br(F)'$，并使用它来提升$\hat{F}$上的不可分解和非交叉积除代数。
英文摘要：
Let T be a complete discrete valuation ring and $\hat{X}$ a smooth projective curve over $S=\spec(T)$ with closed fibre $X$. Denote by $F$ the function field of $\hat{X}$ and by $\hat{F}$ the completion of $F$ with respect to the discrete valuation defined by $X$, the closed fibre. In this paper, we construct indecomposable and noncrossed product division algebras over $F$. This is done by defining an index preserving group homomorphism $s:\br(\hat{F})'\to\br(F)'$, and using it to lift indecomposable and noncrossed product division algebras over $\hat{F}$.
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