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

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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.