Automorphism group functors of algebraic superschemes

The famous theorem of Matsumura–Oort states that if X is a proper scheme, then the automorphism group functor Aut ( X ) of X is a locally algebraic group scheme. In this paper we generalize this theorem to the category of superschemes, that is if X is a proper superscheme, then the automorphism grou...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2024-09, Vol.308 (1), Article 4
Main Author: Zubkov, A. N.
Format: Article
Language:English
Subjects:
Automorphisms
Mathematics
Mathematics and Statistics
Theorems
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Summary:The famous theorem of Matsumura–Oort states that if X is a proper scheme, then the automorphism group functor Aut ( X ) of X is a locally algebraic group scheme. In this paper we generalize this theorem to the category of superschemes, that is if X is a proper superscheme, then the automorphism group functor Aut ( X ) of X is a locally algebraic group superscheme. Moreover, we also show that if H 1 ( X , T X ) = 0 , where X is the geometric counterpart of X and T X is the tangent sheaf of X , then Aut ( X ) is a smooth group superscheme.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-024-03572-y