Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bivariant algebraic cobordism with bundles   The purpose of this paper is to study an extended version of bivariant
derived algebraic cobordism where the cycles carry a vector bundle on the
source as additional data. We show that, over a field of characteristic 0, this
extends the analogous homological theory of Lee and Pandharipande constructed
earlier. We then proceed to study in detail the restricted theory where only
rank 1 vector bundles are allowed, and prove a weak version of projective
bundle formula for bivariant cobordism. Since the proof of this theorem works
very generally, we introduce precobordism theories over arbitrary Noetherian
rings of finite Krull dimension as a reasonable class of theories where the
proof can be carried out, and prove some of their basic properties. These
results can be considered as the first steps towards a Levine-Morel style
algebraic cobordism over a base ring that is not a field of characteristic 0.

15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
16
The categories of this paper are: stat