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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Crystalline Condition for Ainf-cohomology and Ramification Bounds

Pavel Coupek (12464991) 27 April 2022 (has links)
<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>

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