Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sur la cohomologie \`a support des fibr\'es en droites sur les
  vari\'et\'es sym\'etriques compl\`etes   Let $X$ be a complete symmetric variety i.e. the wonderful compactification
of a symmetric $G-$homogeneous space (where $G$ is a simply-connected
semi-simple linear algebraic group). If $L$ is a line bundle over $X$ and if
$C$ is a Bialynicki-Birula cell of codimension $c$ in $X$, then the Lie algebra
$\mathfrak g$ of $G$ operates naturally on the cohomology group with support :
$H^c_C(L)$. One gives here a necessary condition on the cell $C$ for that
$\mathfrak g-$module have a finite dimensional simple subquotient. As
applications one calculates the Euler-Poincar\'e characteristic of $L$ over $X$
and one estimates the higher cohomology group $H^d(X,L)$, $d \ge 0$, with exact
formulae in some cases among which the case of the complete conic variety. --
\'Etant donn\'e un groupe alg\'ebrique lin\'eaire semi-simple G, on
s'int\'eresse aux compactifications magnifiques des G?espaces homog\`enes
sym\'etriques. Si X est une telle compactification, si L est un fibr\'e en
droites G?lin\'earis\'e sur X et si C est une cellule de Bialynicki-Birula de X
de codimension c, alors l'alg\`ebre de Lie g de G op\`ere naturellement sur le
groupe de cohomologie \`a support Hc C (L). On donne ici une condition
n\'ecessaire, portant sur la cellule C, pour que ce g?module poss\`ede un
sous-quotient simple de dimension finie. On en d\'eduit une formule pour la
caract\'eristique d'Euler-Poincar\'e de L sur X et une estimation (exacte pour
certains cas dont celui de la vari\'et\'e des coniques compl\`etes) des groupes
de cohomologie sup\'erieure Hd(X,L), d ? 0.

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The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph