关于半稳定表示格的一个注记

关于特征为2的域上稳定二次多项式的注记

A Note on Stable Quadratic Polynomials over Fields of Characteristic Two

本文首先证明了特征为2的有限域上不存在稳定的二次多项式，然后证明了特征为2的函数域上存在稳定的二次多项式。

Note sur les diviseurs élémentaires du régulateur d'Iwasawa

The article revisits a result of Antonio Lei, David Loeffler, and Sarah Livia Zerbes concerning the structure of the image by the Iwasawa regulator map of the Iwasawa module associated with a semi-stable $p$-adic representation on an unramified finite extension of $Q_p$ and give a direct proof based on the results of "Représentations $p$-adiques et normes universelles: I. le cas cristallin" in the crystalline case and of "Théorie d'Iwasawa des représentations $p$-adiques semi-stables" in the semi-stable case.

Borel's stable range for the cohomology of arithmetic groups

In this note, we remark on the range in Borel's theorem on the stable cohomology of the arithmetic groups Sp(2n,Z) and SO(n,n;Z). This improves the range stated in Borel's original papers, an improvement that was known to Borel. Our main task is a technical computation involving the Weyl group action on roots and weights. This note originally appeared as the appendix to arXiv:1711.03139.