<p>For a prime p>2 and a smooth proper p-adic formal scheme X over O<sub>K</sub> where K is a p-adic field of absolute ramification degree e, we study a series of conditions (Cr<sub>s</sub>), s>=0 that partially control the G<sub>K</sub>-action on the image of the associated Breuil-Kisin prismatic cohomology RΓ<sub>Δ</sub>(X/S) inside the A<sub>inf</sub>-prismatic cohomology RΓ<sub>Δ</sub>(X<sub>Ainf</sub>/A<sub>inf</sub>). The condition (Cr<sub>0</sub>) is a criterion for a Breuil-Kisin-Fargues G<sub>K</sub>-module to induce a crystalline representation used by Gee and Liu, and thus leads to a proof of crystallinity of H<sup>i</sup><sub>et</sub>(X<sub>CK</sub>, Q<sub>p</sub>) that avoids the crystalline comparison. The higher conditions (Cr<sub>s</sub>) are used in an adaptation of a ramification bounds strategy of Caruso and Liu. As a result, we establish ramification bounds for the mod p representations H<sup>i</sup><sub>et</sub>(X<sub>CK</sub>, Z/pZ) for arbitrary e and i, which extend or improve existing bounds in various situations.</p>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/19662252 |
| Date | 27 April 2022 |
| Creators | Pavel Coupek (12464991) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/Crystalline_Condition_for_Ainf-cohomology_and_Ramification_Bounds/19662252 |
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