English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let   k   be a perfect field of characteristic    p  >  2    and   K   an extension of    F  =  Frac  W  (  k  )    contained in some    F  (   μ   p  r    )   . Using crystalline Dieudonné theory, we provide a classification of   p  ‐divisible groups over    R  =   O  K    [   [   t  1   ,  …  ,   t  d   ]   ]in terms of finite height    (  φ  ,  Γ  )   ‐modules over    S  :  =  W   (  k  )   [   [  u  ,   t  1   ,  …  ,   t  d   ]   ]   . When    d  =  0   , such a classification is a consequence of (a special case of) the theory of Kisin–Ren; in this setting, our construction gives an independent proof of this result, and moreover allows us to recover the Dieudonné crystal of a   p  ‐divisible group from the Wach module associated to its Tate module by Berger–Breuil or by Kisin–Ren.

Dieudonné crystals and Wach modules for p ‐divisible groups