Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Shafarevich conjecture and some extension theorems for proper
  hyperbolic polycurves   In this paper, we prove the Shafarevich conjecture for proper hyperbolic
polycurves, which is a higher dimensional analogue of that for proper
hyperbolic curves. First, we study theories of proper hyperbolic polycurves
over regular schemes. For example, we generalize the moduli theory of Kodaira
fibrations due to Jost and Yau. We also show the Neron property of proper
smooth models of proper hyperbolic polycurves over Dedekind schemes under an
assumption on residual characteristics. We then apply these extension theories
to the proof of the Shafarevich conjecture for proper hyperbolic polycurves.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th