Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bloch-Beilinson conjectures for Hecke characters and Eisenstein
  cohomology of Picard surfaces   We consider certain families of Hecke characters $\phi$ over a quadratic
imaginary field $F$. The order of vanishing of the $L$-function $L(\phi,s)$ at
the central point $s=-1$, according to the Beilinson conjectures, should be
equal to the dimension of the space of extensions of the Tate motive
$\mathbb{Q}(1)$ by the motive associated with $\phi$. In this article,
candidates for the corresponding extensions of Hodge structure are constructed,
under the assumptions that the sign of the functional equation of $L(\phi,s)$
is $-1$ and that $L^\prime(\phi,-1) \neq 0$. This is achieved by means of the
cohomology of variations of Hodge structures over Picard modular surfaces
attached to $F$ and Harder's theory of Eisenstein cohomology. Moreover, we
provide a criterion for the non-triviality of these extensions, based on the
non-vanishing of a height pairing that we define and study.

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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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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: solv-int
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The categories of this paper are: plasm-ph