Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform bounds of base change conductors and link with the generalized
  Szpiro conjecture   The difference between the Faltings height of an abelian variety $A$ defined
over a number field $k$ and its stable height is measured by the so-called base
change conductor. In this paper, we give a uniform bound of the base change
conductor in terms of the dimension of $A$ and the degree of $k$. This allows
us to reduce the generalized Szpiro conjecture to the semi-stable case.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat