Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Shafarevich conjecture for hypersurfaces in abelian varieties   Faltings proved that there are finitely many abelian varieties of genus $g$
of a number field $K$, with good reduction outside a finite set of primes $S$.
Fixing one of these abelian varieties $A$, we prove that there are finitely
many smooth hypersurfaces in $A$, with good reduction outside $S$, representing
a given ample class in the Neron-Severi group of $A$, up to translation, as
long as the dimension of $A$ is at least $4$. Our approach builds on the
approach of arXiv:1807.02721 which studies $p$-adic variations of Hodge
structure to turn finiteness results for $p$-adic Galois representations into
geometric finiteness statements. A key new ingredient is an approach to proving
big monodromy for the variations of Hodge structure arising from the middle
cohomology of these hypersurfaces using the Tannakian theory of sheaf
convolution on abelian varieties.

7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs