Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple proof of Tyurin's babylonian tower theorem   Using the method of Coand\u{a} and Trautmann (2006), we give a simple proof
of the following theorem due to Tyurin (1976) in the smooth case: if a vector
bundle $E$ on a $c$-codimensional locally Cohen-Macaulay closed subscheme $X$
of the projective space $P^n$ extends to a vector bundle $F$ on a similar
closed subscheme $Y$ of $P^N$, for every $N > n$, then $E$ is the restriction
to $X$ of a direct sum of line bundles on $P^n$. Using the same method, we also
provide a proof of the Babylonian tower theorem for locally complete
intersection subschemes of projective spaces.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat