Automorphism group functors of algebraic superschemes

A. N. Zubkov

doi:10.1007/s00209-024-03572-y

Automorphism group functors of algebraic superschemes

A. N. Zubkov

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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 H¹(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.

Original language	English
Article number	4
Journal	Mathematische Zeitschrift
Volume	308
Issue number	1
DOIs	https://doi.org/10.1007/s00209-024-03572-y
Publication status	Published - Sept 2024

ASJC Scopus subject areas

General Mathematics

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N2 - 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 H1(X,TX)=0, where X is the geometric counterpart of X and TX is the tangent sheaf of X, then Aut(X) is a smooth group superscheme.

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Automorphism group functors of algebraic superschemes

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