Abstract
AbstractWe study de Rham prismatic crystals on "Equation missing". We show that a de Rham crystal is controlled by a sequence of matrices $$\{A_{m,1}\}_{m \ge 0}$$
{
A
m
,
1
}
m
≥
0
with $$A_{0,1}$$
A
0
,
1
“nilpotent”. Using this, we prove that the natural functor from the category of de Rham crystals over "Equation missing" to the category of nearly de Rham representations is fully faithful. The key ingredient is a Sen style decompletion theorem for $$B_{{\textrm{dR}}}^+$$
B
dR
+
-representations of $$G_K$$
G
K
.
Publisher
Springer Science and Business Media LLC
Reference21 articles.
1. Berger, L., Colmez, P.: Théorie de Sen et vecteurs localement analytiques. Ann. Sci. Éc. Norm. Supér. (4) 49(4), 947–970 (2016)
2. Berger, L.: Multivariable $$(\varphi ,\Gamma )$$-modules and locally analytic vectors. Duke Math. J. 165(18), 3567–3595 (2016)
3. Bhatt, B., Scholze, P.: The pro-étale topology for schemes. arXiv preprint arXiv:1309.1198 (2013)
4. Bhatt, B., Scholze, P.: Prisms and prismatic cohomology. arXiv:1905.08229 (2019)
5. Bhatt, B., Scholze, P.: Prismatic $$ F $$-crystals and crystalline Galois representations. arXiv preprint arXiv:2106.14735 (2021)