Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hermitian K-theory, derived equivalences and Karoubi's Fundamental
  Theorem   Within the framework of dg categories with weak equivalences and duality that
have uniquely 2-divisible mapping complexes, we show that higher
Grothendieck-Witt groups (aka. hermitian K-groups) are invariant under derived
equivalences and that Morita exact sequences induce long exact sequences of
Grothendieck-Witt groups. This implies an algebraic Bott sequence and a new
proof and generalization of Karoubi's Fundamental Theorem. For the higher
Grothendieck-Witt groups of vector bundles of (possibly singular) schemes with
an ample family of line-bundles such that 2 is invertible in the ring of
regular functions, we obtain Mayer-Vietoris long exact sequences for Nisnevich
coverings and blow-ups along regularly embedded centers, projective bundle
formulas, and a Bass fundamental theorem. For coherent Grothendieck-Witt
groups, we obtain a localization theorem analogous to Quillen's K'-localization
theorem.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int