Class number formula over global field of characteristic p and with coefficients.

在2022-23学年，我们完成了一篇关于阿贝尔变分的mu不变量在函数域上的变化的研究论文。该论文现已提交，并可在此地址https://arxiv.org/abs/2301.09073获得。除此之外，我们尝试将Brinon-T方法推广到伽罗瓦等变版本。我们面临着一个困难：那里的建筑功能不够。因此，我们理解了首先加强Brinon-T结构建设的重要性。另一方面，我们现在有了一个与自同构p进系数有关的推测p进l函数的公式。2023年3月，我们在班加罗尔的印度科学院做了一个关于这个问题的演讲。

During the academic year 2022-23 we were able to complete one paper on the study of the variation of the mu-invariant of abelian variety over function field. The paper is now submitted and available at this address https://arxiv.org/abs/2301.09073 . Besides this, we tried to extend the method of Brinon-T to a Galois equivariant version. We are facing a difficulty : the construction there is not functorial enough. Therefore, we understood the importance of strengthening first the construction of Brinon-T. On an other hand, we have now the formulation for a conjectural p-adic L-function attached to automorphic p-adic coefficients. We have done a talk about this at the IISc Bangalore in March 2023.