Modular variants of p-adic fundamental sequence

Abstract

In this article, we relate any Farey triangle in the extended upper half-plane to a variant of Colmez--Fontaine's fundamental lemma in $p$-adic Hodge theory. In particular, their original fundamental lemma corresponds to the fundamental Farey triangle $(\frac{1}{0},\frac{1}{1},\frac{0}{1})$.

11 pages, 1 figure. arXiv:2404.04551v1 has been split into two papers; this is the first part. All comments are welcome!