An explicit example of a noncrossed product division algebra
... There is a result6 that limits the hope of finding an explicit noncrossed product example of the form D(x, σ) : If D is a quaternion algebra over a local or global field then any D(x, σ) is a crossed product. With this result in mind, it is clear that even though we do not achieve the smallest possi ...
... There is a result6 that limits the hope of finding an explicit noncrossed product example of the form D(x, σ) : If D is a quaternion algebra over a local or global field then any D(x, σ) is a crossed product. With this result in mind, it is clear that even though we do not achieve the smallest possi ...
Finite group schemes
... It is natural to ask if Gred is carries a natural group scheme structure over k. In general the answer is no. However, if we assume k is perfect, the answer is yes. Since Gred is reduced, it is smooth (the theorem on connected components), and therefore geometrically reduced (again the theorem). By ...
... It is natural to ask if Gred is carries a natural group scheme structure over k. In general the answer is no. However, if we assume k is perfect, the answer is yes. Since Gred is reduced, it is smooth (the theorem on connected components), and therefore geometrically reduced (again the theorem). By ...
