Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Shimura varieties in the Torelli locus via Galois coverings of elliptic
  curves   We study Shimura subvarieties of $\mathsf{A}_g$ obtained from families of
Galois coverings $f: C \rightarrow C'$ where $C'$ is a smooth complex
projective curve of genus $g' \geq 1$ and $g= g(C)$. We give the complete list
of all such families that satisfy a simple sufficient condition that ensures
that the closure of the image of the family via the Torelli map yields a
Shimura subvariety of $\mathsf{A}_g$ for $g' =1,2$ and for all $g \geq 2,4$ and
for $g' > 2$ and $g \leq 9$. In a previous work of the first and second author
together with A. Ghigi [FGP] similar computations were done in the case $g'=0$.
Here we find 6 families of Galois coverings, all with $g' = 1$ and $g=2,3,4$
and we show that these are the only families with $g'=1$ satisfying this
sufficient condition. We show that among these examples two families yield new
Shimura subvarieties of $\mathsf{A}_g$, while the other examples arise from
certain Shimura subvarieties of $\mathsf{A}_g$ already obtained as families of
Galois coverings of $\mathbb{P}^1$ in [FGP]. Finally we prove that if a family
satisfies this sufficient condition with $g'\geq 1$, then $g \leq 6g'+1$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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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: math-ph
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The categories of this paper are: hep-ph