-neighborhoods and comparison theorems
2015 ◽
Vol 151
(10)
◽
pp. 1945-1964
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Keyword(s):
A technical ingredient in Faltings’ original approach to$p$-adic comparison theorems involves the construction of$K({\it\pi},1)$-neighborhoods for a smooth scheme$X$over a mixed characteristic discrete valuation ring with a perfect residue field: every point$x\in X$has an open neighborhood$U$whose generic fiber is a$K({\it\pi},1)$scheme (a notion analogous to having a contractible universal cover). We show how to extend this result to the logarithmically smooth case, which might help to simplify some proofs in$p$-adic Hodge theory. The main ingredient of the proof is a variant of a trick of Nagata used in his proof of the Noether normalization lemma.
2011 ◽
Vol 147
(6)
◽
pp. 1772-1792
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Keyword(s):
2011 ◽
Vol 148
(1)
◽
pp. 227-268
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Keyword(s):
2010 ◽
Vol 20
(01)
◽
pp. 27-38
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2018 ◽
Vol 17
(08)
◽
pp. 1850160
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Keyword(s):