Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness results for finite flat group schemes over discrete
  valuation rings of mixed characteristic   Let $p$ be a prime. Let $V$ be a discrete valuation ring of mixed
characteristic $(0,p)$ and index of ramification $e$. Let $f: G \rightarrow H$
be a homomorphism of finite flat commutative group schemes of $p$ power order
over $V$ whose generic fiber is an isomorphism. We provide a new proof of a
result of Bondarko and Liu that bounds the kernel and the cokernel of the
special fiber of $f$ in terms of $e$. For $e < p-1$ this reproves a result of
Raynaud. Our bounds are sharper that the ones of Liu, are almost as sharp as
the ones of Bondarko, and involve a very simple and short method. As an
application we obtain a new proof of an extension theorem for homomorphisms of
truncated Barsotti--Tate groups which strengthens Tate's extension theorem for
homomorphisms of $p$-divisible groups.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys