Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sur la compatibilit\'e \`a Frobenius de l'isomorphisme de dualit\'e
  relative   Let $\V$ be a mixed characteristic complete discrete valuation ring, let $\X$
and $\Y$ be two smooth formal $\V$-schemes, let $f_0$ : $X \to Y$ be a
projective morphism between their special fibers, let $T$ be a divisor of $Y$
such that $T_X := f_0 ^{-1} (T) $ is a divisor of $X$ and let $\M \in D
^\mathrm{b}_\mathrm{coh} (\D ^\dag_{\X} (\hdag T_X)_{\Q})$. We construct the
relative duality isomorphism $ f_{0T +} \circ \DD_{\X, T_X} (\M) \riso \DD_{\Y,
T} \circ f_{0T +} (\M)$. This generalizes the known case when there exists a
lifting $f : \X \to \Y$ of $f_{0}$. Moreover, when $f_0$ is a closed immersion,
we prove that this isomorphism commutes with Frobenius.

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The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
9
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: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th