TY - JOUR
T1 - Automorphism group functors of algebraic superschemes
AU - Zubkov, A. N.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
PY - 2024/9
Y1 - 2024/9
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.
AB - 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.
UR - https://www.scopus.com/pages/publications/85199757591
UR - https://www.scopus.com/pages/publications/85199757591#tab=citedBy
U2 - 10.1007/s00209-024-03572-y
DO - 10.1007/s00209-024-03572-y
M3 - Article
AN - SCOPUS:85199757591
SN - 0025-5874
VL - 308
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1
M1 - 4
ER -