Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First cohomology groups for finite groups of Lie type in defining
  characteristic   Let G be a finite group of Lie type, defined over a field k of characteristic
p > 0. We find explicit bounds for the dimension of the first cohomology group
for G with coefficients in a simple kG-module. We proceed by bounding the
number of composition factors of Weyl modules for simple algebraic groups
independently of p and using this to deduce bounds for the 1-cohomology of
simple algebraic groups. Finally, we use this to obtain estimations for the
growth rate of the maximum dimension {\gamma_l} of these 1-cohomology groups
over all groups of Lie type of rank l. We find that log \gamma_l is O(l^3 log
l) (or if the Lusztig conjecture holds, O(l^2 log l)).

27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an