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摘要翻译：
在char$k=p>0$中，a.Langer证明了半可定束在某些变体上对一个非常一般的D$次超曲面的一个强限制定理（采用H.Flenner的风格），条件是:char$k>D$'。他指出，为了消除这个条件，只要肯定地回答以下任何一个问题就足够了：{\对于${\mathcal O}(d)$的syzygy束$\sv_d$来说，$\sv_d$对于任意的$n、d$和$p={char}k$是半稳定的吗？或者对$\mu_{max}(\sv_d^*)$有一个好的估计吗？}本文证明了:(1)$\sv_d$是半可集，对于某个无穷大的整数集$d\geq0$；（2）对于任意的$d$,在$d$和$n$方面对$\mu_{max}(\sv_d^*)$有足够好的估计。特别地，我们得到了任意特征的兰格定理。
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英文标题：
《Semistablity of syzygy bundles on projective spaces in positive
characteristics》
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作者：
V. Trivedi
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最新提交年份：
2009
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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：Representation Theory 表象理论
分类描述：Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra
代数和群的线性表示，李理论，结合代数，多重线性代数
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英文摘要：
In char $k = p >0$, A. Langer proved a strong restriction theorem (in the style of H. Flenner) for semistable sheaves to a very general hypersurface of degree $d$, on certain varieties, with the condition that `char $k > d$'. He remarked that to remove this condition, it is enough to answer either of the following questions affirmatively: {\it For the syzygy bundle $\sV_d$ of ${\mathcal O}(d)$, is $\sV_d$ semistable for arbitrary $n, d$ and $p = {char} k$?, or is there a good estimate on $\mu_{max}(\sV_d^*)$?} Here we prove that (1) the bundle $\sV_d$ is semistable, for a certain infinite set of integers $d\geq 0$, and (2) for arbitrary $d$, there is a good enough estimate on $\mu_{max}(\sV_d^*)$ in terms of $d$ and $n$. In particular one obtains Langer's theorem, in arbitrary characeristic.
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PDF链接：
https://arxiv.org/pdf/0804.0547
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