Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Grothendieck--Serre's conjecture concerning principal G-bundles over
  reductive group schemes:II   A proof of Grothendieck--Serre conjecture on principal bundles over a
semi-local regular ring containing an infinite field is given in [FP] recently.
That proof is based significantly on Theorem 1.0.1 stated below in the
Introduction and proven in the present preprint. Theorem 1.0.1 itself is a
consequence of two purity theorems (Theorems A and 10.0.30) proven below in the
present preprint. The geometric part of a new preprint [PSV] and the main
result of an article [C-T-S] are used significantly in proofs of those two
purity theorems.
  One of that purity result looks as follows. Let O be a semi-local ring of
finitely many closed points on a k-smooth irreducible affine scheme, where k is
an infinite field. Given a smooth O-group scheme morphism mu G to C of
reductive O-group schemes, with a torus C one can form a functor from
O-algebras to abelian groups, which takes an O-algebra S to the quotient group
F(S)=C(S) modulo mu(G(S)). Assuming additionally that the kernel of mu is a
reductive O-group scheme, we prove that this functor satisfies a purity theorem
for the k-algebra O.
  Examples to mentioned purity results are considered at the very end of the
preprint.

24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics