Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniformizing the Stacks of Abelian Sheaves   Elliptic sheaves (which are related to Drinfeld modules) were introduced by
Drinfeld and further studied by Laumon--Rapoport--Stuhler and others. They can
be viewed as function field analogues of elliptic curves and hence are objects
"of dimension 1". Their higher dimensional generalisations are called abelian
sheaves. In the analogy between function fields and number fields, abelian
sheaves are counterparts of abelian varieties. In this article we study the
moduli spaces of abelian sheaves and prove that they are algebraic stacks. We
further transfer results of Cerednik--Drinfeld and Rapoport--Zink on the
uniformization of Shimura varieties to the setting of abelian sheaves. Actually
the analogy of the Cerednik--Drinfeld uniformization is nothing but the
uniformization of the moduli schemes of Drinfeld modules by the Drinfeld upper
half space. Our results generalise this uniformization. The proof closely
follows the ideas of Rapoport--Zink. In particular, analogies of $p$-divisible
groups play an important role. As a crucial intermediate step we prove that in
a family of abelian sheaves with good reduction at infinity, the set of points
where the abelian sheaf is uniformizable in the sense of Anderson, is formally
closed.

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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph