Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The topological Hochschild homology of algebraic $K$-theory of finite
  fields   Let $K(\mathbb{F}_q)$ be the algebraic $K$-theory spectrum of the finite
field with $q$ elements and let $p \geq 5$ be a prime number coprime to $q$. In
this paper we study the mod $p$ and $v_1$ topological Hochschild homology of
$K(\mathbb{F}_q)$, denoted $V(1)_*THH(K(\mathbb{F}_q))$, as an
$\mathbb{F}_p$-algebra. The computations are organized in four different cases,
depending on the mod $p$ behaviour of the function $q^n-1$. We use different
spectral sequences, in particular the B\"okstedt spectral sequence and a
generalization of a spectral sequence of Brun developed in an earlier paper. We
calculate the $\mathbb{F}_p$-algebras $THH_*(K(\mathbb{F}_q); H\mathbb{F}_p)$,
and we compute $V(1)_*THH(K(\mathbb{F}_q))$ in the first two cases.

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom