关于等对偶格的斜率

摘要：

欧氏格的斜率滤子在20世纪70年代末由Stuhler在其著作中引入，几年后由Grayson扩展，作为约化理论及其在算术群研究中的应用的新工具。具有平凡滤子的格称为半稳定格，这与经典术语一致。1997年，Bost证明了半稳定格的张量积本身也是半稳定的。我们在这项工作中的目的是研究这些问题的限制类的isodual格。这样的格子出现在广泛的背景下，研究它们的斜率过滤是很自然的。在这种情况下，我们表现出特定的属性，从而允许，反过来，证明一些新的特殊情况下博斯特猜想。

英文摘要：

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.

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