On the Grothendieck-Serre Conjecture about principal bundles and its generalizations
Roman Fedorov

TL;DR
This paper proves a significant case of the Grothendieck-Serre conjecture for principal bundles over semi-local schemes, extending results to arbitrary reductive group schemes and simplifying existing proofs.
Contribution
It establishes the triviality of principal G-bundles over semi-local schemes under certain conditions and generalizes previous results from simple simply-connected groups to all reductive groups.
Findings
Principal G-bundles trivial over generic fibers are trivial over the entire scheme.
The proof of the Grothendieck-Serre conjecture is simplified.
Results extended from simple simply-connected groups to all reductive groups.
Abstract
Let be a regular connected affine semi-local scheme over a field . Let be a reductive group scheme over . Assuming that has an appropriate parabolic subgroup scheme, we prove the following statement. Given an affine -scheme , a principal -bundle over is trivial if it is trivial over the generic fiber of the projection . We also simplify the proof of the Grothendieck-Serre conjecture: let be a regular connected affine semi-local scheme over a field . Let be a reductive group scheme over . A principal -bundle over is trivial if it is trivial over the generic point of . We generalize some other related results from the simple simply-connected case to the case of arbitrary reductive group schemes.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
