Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the K-theory of pullbacks   To any pullback square of ring spectra we associate a new ring spectrum and
use it to describe the failure of excision in algebraic $K$-theory. The
construction of this new ring spectrum is categorical and hence allows to
determine the failure of excision for any localizing invariant in place of
$K$-theory.
  As immediate consequences we obtain an improved version of Suslin's excision
result in $K$-theory, generalizations of results of Geisser and Hesselholt on
torsion in (bi)relative $K$-groups, and a generalized version of pro-excision
for $K$-theory. Furthermore, we show that any truncating invariant satisfies
excision, nilinvariance, and cdh-descent. Examples of truncating invariants
include the fibre of the cyclotomic trace, the fibre of the rational
Goodwillie--Jones Chern character, periodic cyclic homology in characteristic
zero, and homotopy $K$-theory.
  Various of the results we obtain have been known previously, though most of
them in weaker forms and with less direct proofs.

26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci