Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Comparison of Two Complexes   In this paper we prove the conjecture of Lusztig in "Generic character
sheaves on groups over $\mathbf{k}[\epsilon]/(\epsilon^r)$." Given a reductive
group over $\mathbb{F}_q$ for some $r\geq 2$, there is a notion of a character
sheaf defined in "Character sheaves and generalizations" by Lusztig. On the
other hand, there is also a geometric analogue of the character constructed by
G\'erardin. The conjecture states that the two constructions are equivalent,
which Lusztig also proved for $r=2, 3, 4$. Here we generalize his method to
prove this conjecture for general $r$. As a corollary we prove that the
characters derived from these two complexes are equal.

21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn