Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relative geometries   We start an analysis of geometric properties of a structure relative to a
reduct. In particular, we look at definability of groups and fields in this
context. In the relatively one-based case, every definable group is isogenous
to a subgroup of a product of groups definable in the reducts. In the
relatively CM-trivial case, which contains certain Hrushovski amalgamations
(the fusion of two strongly minimal sets or the expansions of a field by a
predicate), every definable group allows a homomorphism with virtually central
kernel into a product of groups definable in the reducts.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys