论文标题
在异想曲晶格的斜坡上
On slopes of isodual lattices
论文作者
论文摘要
Stuhler在1970年代后期的作品中引入了欧几里得格的斜率过滤，几年后，格雷森（Grayson）扩展了，作为还原理论的新工具及其在算术群体研究中的应用。与经典术语保持一致，具有微不足道的过滤的晶格称为半固定。 1997年，BOST猜想，可半固定的晶格的张量应该是半固定的。我们在这项工作中的目的是研究这些问题的疑受限型晶格类别。这样的晶格出现在各种环境中，研究其斜率过滤是很自然的。在这种情况下，我们表现出特定的特性，从而允许证明BOST的一些新特定案例。
The slope filtration of Euclidean lattices was introduced in works by Stuhler in the late 1970s, extended by Grayson a few years later, as a new tool for reduction theory and its applications to the study of arithmetic groups. Lattices with trivial filtration are called semistable, in keeping with a classical terminology. In 1997, Bost conjectured that the tensor product of semistable lattices should be semistable itself. Our aim in this work is to study these questions for the restricted class of isodual lattices. Such lattices appear in a wide range of contexts, and it is rather natural to study their slope filtration. We exhibit specific properties in this case, which allow, in turn, to prove some new particular cases of Bost's conjecture.
