Leírás
Abstract:
The purpose of my talk is to introduce the concept of Harish-Chandra pair and its applications in the theory of (not necessary affine) group superschemes. In collaboration with A. Masuoka, we have proved that the category of (locally algebraic) group superschemes is naturally equivalent to the category of certain Harish-Chandra pairs. Then, using this fundamental equivalence, we proved a superversion of the famous Barsotti-Chevalley theorem. Besides, we also proved that a sheaf quotient of an algebraic group superscheme over its group super-subscheme is again a superscheme of finite type.
The above mentioned applications are just first evidences of the power of the method of Harish-Chandra pairs and I will discuss the problems which could be attacked with the help of it in future.
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