Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Note on linear relations in Galois cohomology and {\'e}tale $K$-theory
  of curves   In this paper we investigate a local to global principle for Galois
cohomology of number fields with coefficients in the Tate module of an abelian
variety. In \cite{bk13} G. Banaszak and the author obtained the sufficient
condition for the validity of the local to global principle for {\'e}tale
$K$-theory of a curve . This condition in fact has been established by means of
an analysis of the corresponding problem in the Galois cohomology. We show that
in some cases this result is the best possible i.e if this condition does not
hold we obtain counterexamples.
  We also give some examples of curves and their Jacobians. Finally, we prove
the dynamical version of the local to global principle for {\'e}tale $K$-theory
of a curve. The dynamical local to global principle for the groups of
Mordell-Weil type has recently been considered by S. Bara{\'n}czuk in
\cite{b17}. We show that all our results remain valid for Quillen $K$-theory of
${\cal X}$ if the Bass and Quillen-Lichtenbaum conjectures hold true for ${\cal
X}.$

4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat