Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mixed Hodge structures and representations of fundamental groups of
  algebraic varieties   Given a complex variety $X$, a linear algebraic group $G$ and a
representation $\rho$ of the fundamental group $\pi\_1(X,x)$ into $G$, we
develop a framework for constructing a functorial mixed Hodge structure on the
formal local ring of the representation variety of $\pi\_1(X,x)$ into $G$ at
$\rho$ using mixed Hodgediagrams and methods of $L\_\infty$ algebras. We apply
it in two geometric situations: either when $X$ is compact K{\"a}hler and
$\rho$ is the monodromy of a variation of Hodge structure, or when $X$ is
smooth quasi-projective and $\rho$ has finite image.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio