Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $K(\pi, 1)$-neighborhoods and comparison theorems   A technical ingredient in Faltings' original approach to p-adic comparison
theorems involves the construction of $K(\pi, 1)$-neighborhoods for a smooth
scheme X over a mixed characteristic dvr with a perfect residue field: every
point of X has an open neighborhood whose general fiber is a $K(\pi, 1)$ 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.

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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci