Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometry of global function fields, the Riemann-Roch theorem, and
  finiteness properties of S-arithmetic groups   Harder's reduction theory provides filtrations of euclidean buildings that
allow one to deduce cohomological and homological properties of S-arithmetic
groups over global function fields. In this survey I will sketch the main
points of Harder's reduction theory starting from Weil's geometry of numbers
and the Riemann-Roch theorem, describe a filtration that is particularly useful
for deriving finiteness properties of S-arithmetic groups, and state the rank
conjecture and its partial verifications that do not restrict the cardinality
of the underlying field of constants. As a motivation for further research I
also state a much more general conjecture on isoperimetric properties of
S-arithmetic groups over global fields (number fields or function fields).

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int