Extension theorems for reductive group schemes

Abstract

We prove several basic extension theorems for reductive group schemes. We also prove that each Lie algebra with a perfect Killing form over a commutative $\dbZ$-algebra, is the Lie algebra of an adjoint group scheme.

22 pages, accepted for publication in final form. To appear in Algebra & Number Theory

References in corpus (3)

• On two theorems for flat, affine group schemes over a discrete valuation ring
• A purity theorem for abelian schemes
• Three methods to prove the existence of integral canonical models of Shimura varieties of Hodge type

Cited by in corpus (3)

• Good reductions of Shimura varieties of Hodge type in arbitrary unramified mixed characteristic. Part I
• $E_8$ and the average size of the 3-Selmer group of the Jacobian of a pointed genus-2 curve
• On Lie algebra modules which are modules over semisimple group schemes