43 citations · 207 across the 45 of their papers we have counts for
52 papers
On the Gille theorem for the relative projective line
Ivan Panin, Anastasia Stavrova
Let be a Noetherian separated scheme. Let be a reductive -group scheme, and let be a principal -bundle over . We prove that if the restriction of…
On the Gille theorem for the relative projective line: I
Ivan Panin, Anastasia Stavrova
We prove a relative version of a theorem on torsors on the projective line due to Philippe Gille. As a consequence we obtain a ``weak homotopy invariance'' result for torsors under…
Pfister forms and a conjecture due to Colliot-Thélène in the mixed characteristic case
Ivan Panin, Dimitrii Tyurin
let be a regular local ring of a mixed characteristic where is a prime number. Suppose that the quotient ring is also regular. Fix a non-degenerate Pfi…
On the Grothendieck--Serre conjecture for projective smooth schemes over a DVR
Ning Guo, Ivan Panin
The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group scheme over a regular local ring is trivial. The mixed characteris…
Weak elementary fibrations
Ning Guo, Ivan Panin
We introduce a notion of a weak elementary fibration and prove that it does exist in certain interesting cases. Our notion is a modification of the M. Artin's notion of an elementa…
A presentation theorem for smooth projective schemes over discrete valuation rings
Ning Guo, Ivan Panin
In this article, we give a proof for a geometric presentation theorem for any irreducible scheme smooth projective over a discrete valuation ring . As a consequence, for any…