1. On the Grothendieck–Serre conjecture on principal bundles in mixed characteristic
- Author
-
Roman Fedorov
- Subjects
Large class ,Pure mathematics ,Conjecture ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Principal (computer security) ,Local ring ,Field (mathematics) ,Regular local ring ,Mathematics - Commutative Algebra ,Commutative Algebra (math.AC) ,16. Peace & justice ,01 natural sciences ,Mathematics - Algebraic Geometry ,Scheme (mathematics) ,FOS: Mathematics ,0101 mathematics ,Algebraic Geometry (math.AG) ,Quotient ,Mathematics - Abstract
Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. We prove the conjecture for a large class of regular local rings not containing fields in the case when G is split., Comment: The final version to be published in Transactions of the AMS. Results about quadratic forms are strengthened. In the section on Bertini type theorems a correction in the case of a non-perfect residue field is made. Other minor corrections and improvements
- Published
- 2021