Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: No phantoms in the derived category of curves over arbitrary fields, and
  derived characterizations of Brauer-Severi varieties   In this paper we show that the derived category of Brauer-Severi curves
satisfies the Jordan-H\"older property and cannot have quasi-phantoms, phantoms
or universal phantoms. In this way we obtain that quasi-phantoms, phantoms or
universal phantoms cannot exist in the derived category of smooth projective
curves over a field $k$. Moreover, we show that a $n$-dimensional Brauer-Severi
variety is completely characterized by the existence of a full weak exceptional
collection consisting of pure vector bundles of length $n+1$, at least in
characteristic zero. We conjecture that Brauer-Severi varieties $X$ satisfy
$\mathrm{rdim}_{\mathrm{cat}}(X)=\mathrm{ind}(X)-1$, provided period equals
index, and prove this in the case of curves, surfaces and for Brauer-Severi
varieties of index at most three. We believe that the results for curves are
known to the experts. We nevertheless give the proofs, adding to the
literature.

37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat