Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Galois group of the category of mixed Hodge-Tate structures   The category of rational mixed Hodge-Tate structures is a mixed Tate
category. So thanks to the Tannakian formalism, it is equivalent to the
category of finite dimensional graded comodules over a graded commutative Hopf
algebra H over Q. Since the category has homological dimension 1, the Hopf
algebra H is isomorphic to the commutative graded Hopf algebra provided by the
tensor algebra of the graded vector space given by the direct sum of the groups
C/Q(n) over n>0. However this isomorphism is not natural in any sense, e.g.
does not work in families.
  We give a natural explicit construction of the Hopf algebra H.
  Generalizing this, we define a Hopf dg-algebra related to any dg-algebra R
over a field k, equipped with an invertible line k(1). When R is the sheaf of
algebras given by the holomorphic de Rham complex of a complex manifold X, and
the line is Q(1), the related Hopf dg-algebra describes a dg-model of the
derived category of variations of Hodge-Tate structures on X. Its cobar complex
provides a dg-model for the rational Deligne cohomology of X.
  We consider a variant of our construction which starts from Fontaine's
crystalline / semi-stable period rings and produces graded / dg Hopf algebras,
which we relate to the p-adic Hodge theory.

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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: econ
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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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: funct-an
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The categories of this paper are: plasm-ph
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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: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys