Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Eisenstein-Kronecker classes, integrality of critical values of Hecke
  $L$-functions and $p$-adic interpolation   We show that for an arbitrary totally complex number field $L$ the
(regularized) critical $L$-values of algebraic Hecke characters of $L$ divided
by certain periods are algebraic integers. This relies on a new construction of
an equivariant coherent cohomology class with values in the completion of the
Poincar\'e bundle on an abelian scheme $\cal{A}$. From this we obtain a
cohomology class for the automorphism group of a CM abelian scheme $\cal{A}$
with values in some canonical bundles, which can be explicitly calculated in
terms of Eisenstein-Kronecker series. As a further consequence, using an
infinitesimal trivialization of the Poincar\'e bundle, we construct a $p$-adic
measure interpolating the critical $L$-values in the ordinary case. This
generalizes previous results for CM fields by Damerell, Shimura and Katz and
settles the algebraicity and $p$-adic interpolation in the remaining open cases
of critical values of Hecke $L$-functions.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an