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Fontaine describes in §2 of this old survey work by Wintenberger and wonders (on p. 97) that the structures found by Wintenberger are a "complete mystery" and no-one knows a "reasonable geometric interpretation". Is that still a mystery?

Thomas Riepe
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    Perhaps it would help if you mentioned that the structures in question are canonical $\mathbb{Z}_p$-integral structures on the de Rham cohomology of a smooth proper scheme over $W$, the ring of Witt vectors over a perfect field of characteristic $p$. – S. Carnahan Mar 18 '11 at 13:44
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    Please read the "how to ask" page, even if you have done so before. – S. Carnahan Mar 18 '11 at 13:45
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    Thanks Scott, but what should be the mystery? Did you read Winterberger's articles? (I didn't) – Thomas Riepe Mar 18 '11 at 20:36
  • The link to springerlink.com is dead. I'm also unable to find any snapshot saved on the Wayback Machine. – The Amplitwist Nov 11 '22 at 09:55

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