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摘要翻译：
我们利用扭束来研究Brauer类的指数约简问题。一般说来，这个问题可以这样表述：给定一个字段$k$、一个$k$-Variety$X$和一个类$\alpha\In\br(k)$,通过将标量扩展到$k(X)$来计算类$\alpha_{k(X)}\In\br(X)$的索引。本文给出了计算指数约简的一般方法，它改进了Schofield和van den Bergh的经典结果。当$x$是亏格1的曲线时，我们利用Atiyah关于积分斜率稳定向量丛结构的定理，证明了我们的公式大大简化，给出了这种情况下指数约简问题的完全解。利用扭曲Fourier-Mukai变换，我们证明了一个类似简单的公式描述了高维阿贝尔变体下torsors上的齐次折射率约化。
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英文标题：
《Index reduction for Brauer classes via stable sheaves (with an appendix
by Bhargav Bhatt)》
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作者：
Daniel Krashen and Max Lieblich
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Rings and Algebras 环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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英文摘要：
We use twisted sheaves to study the problem of index reduction for Brauer classes. In general terms, this problem may be phrased as follows: given a field $k$, a $k$-variety $X$, and a class $\alpha \in \Br(k)$, compute the index of the class $\alpha_{k(X)} \in \Br(X)$ obtained from $\alpha$ by extension of scalars to $k(X)$. We give a general method for computing index reduction which refines classical results of Schofield and van den Bergh. When $X$ is a curve of genus 1, we use Atiyah's theorem on the structure of stable vector bundles with integral slope to show that our formula simplifies dramatically, giving a complete solution to the index reduction problem in this case. Using the twisted Fourier-Mukai transform, we show that a similarly simple formula describes homogeneous index reduction on torsors under higher-dimensional abelian varieties.
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PDF链接：
https://arxiv.org/pdf/0706.1072
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