Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Base change for semiorthogonal decompositions   Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base
change $T \to S$. Given an admissible subcategory $\CA$ in the bounded derived
category of coherent sheaves on $X$, we construct an admissible subcategory in
the bounded derived category of coherent sheaves on the fiber product
$X\times_S T$, called the base change of $\CA$, in such a way that the
following base change theorem holds: if a semiorthogonal decomposition of the
bounded derived category of $X$ is given then the base changes of its
components form a semiorthogonal decomposition of the bounded derived category
of the fiber product. As an intermediate step we construct a compatible system
of semiorthogonal decompositions of the unbounded derived category of
quasicoherent sheaves on $X$ and of the category of perfect complexes on $X$.
As an application we prove that the projection functors of a semiorthogonal
decomposition are kernel functors.

16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin