Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some computations with the $\mathscr{F}$-homotopy limit spectral
  sequence   The uniform $\mathcal{F}_p$-isomorphism theorem of Quillen gives a comparison
map between the Borel equivariant $\mathbf{Z}/p$-cohomology of a space and a
limit involving only the Borel equivariant cohomology groups of the same space
with the action restricted to the elementary abelian $p$-subgroups. The theorem
states that the elements in the kernel are nilpotent, and that every element in
the codomain has a power that is in the image. By work of Mathew-Naumann-Noel,
for a fixed group and an arbitrary space, there is a uniform bound on the
nilpotence degree of the elements in the kernel, and on the power necessary to
raise an element in the codomain by to get an element in the image. Using their
methods, we give for $p=2$ explicit upper bounds for finite groups with 2-Sylow
of order less than or equal to 16. In particular, we show that the elements in
the kernel have in that case nilpotence degree less than or equal to 4, and
every element in the codomain raised to the power 8 is in the image. We do this
by bounding from above the $\mathscr{E}_{(2)}$-exponent, as defined by
Mathew-Naumann-Noel, of Borel equivariant singular $\mathbf{Z}/2$-cohomology
for the 2-groups of order less than or equal to 16. We also bound the exponent
from below by evaluating a homotopy limit spectral sequence for all these
groups.

10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat