Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Full faithfulness without Frobenius structure and partially overcoherent
  isocrystals   Let $K$ be a mixed characteristic complete discrete valuation field with
perfect residue field $k$. Let $X$ be a variety over $k$, $Y$ be an open of
$X$, $Y'$ be an open of $Y$ dense in $X$. We extend Kedlaya's full faithfulness
as follows (we do not suppose $Y$ to be smooth): the canonical functor
$F\text{-}\mathrm{Isoc} ^{\dag} (Y,X/K) \to F\text{-}\mathrm{Isoc} ^{\dag}
(Y,Y/K) $ is fully faithfull.
  Suppose now $Y$ smooth. We construct the category of partially overcoherent
isocrystals over $(Y,X)$ denoted by $\mathrm{Isoc} ^{\dag\dag} (Y,X/K) $ whose
objects are some particular arithmetic $\D$-modules. Furthermore, we check the
equivalence of categories $\sp_{(Y,X),+} : \mathrm{Isoc} ^{\dag} (Y,X/K) \cong
\mathrm{Isoc} ^{\dag\dag} (Y,X/K)$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph