摘要翻译：
利用关于环面作用的等变$K$-理论的分圆专门化，我们在一类包含Grassmannian和光滑二次曲面的变体上，导出了相干束的导出范畴中例外对象的离散不变量的同余式。例如，我们证明了如果$x={\bbb P}^{n_1-1}\times...\times{\bbb P}^{n_k-1}$,其中$n_i$是固定素数$P$的幂，则$x$上异常对象的秩与$\pm1$模$P$同余。
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英文标题：
《K-theoretic exceptional collections at roots of unity》
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作者：
Alexander Polishchuk
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最新提交年份：
2008
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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：K-Theory and Homology        K-理论与同调
分类描述：Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论，与拓扑的关系，交换代数和算子代数
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英文摘要：
  Using cyclotomic specializations of the equivariant $K$-theory with respect to a torus action we derive congruences for discrete invariants of exceptional objects in derived categories of coherent sheaves on a class of varieties that includes Grassmannians and smooth quadrics. For example, we prove that if $X={\Bbb P}^{n_1-1}\times...\times{\Bbb P}^{n_k-1}$, where $n_i$'s are powers of a fixed prime number $p$, then the rank of an exceptional object on $X$ is congruent to $\pm 1$ modulo $p$.
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PDF链接：
https://arxiv.org/pdf/0809.1194