Year: 2021
Type: preprint
Abstract: We prove that a Hodge--Tate prismatic crystal on (O_K)_{\Prism} is uniquely determined by a topologically "nilpotent" operator. Using this operator, we construct a C_p-representation of G_K from a Hodge--Tate crystal in an explicit way. We then compute the cohomology of a Hodge--Tate crystal by using this operator and obtain the cohomological dimension of a crystal. In particular, we conjecture that this operator is essentially the classical Sen operator. As applications, under some mild assumption, we show the crystalline Breuil--Kisin modules admit "nilpotent connections" and give an explicit description of prismatic crystals. This "connection" is conjectured predicting the Hodge--Tate weights of associated crystalline representations.
Source: arXiv (Cornell University)
Authors: Min, Yu, Wang, Yupeng
Institutions: Imperial College London, Chinese Academy of Sciences
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4225635271