TY - JOUR
T1 - EQUIVARIANT MODELS OF SPHERICAL VARIETIES
AU - Borovoi, Mikhail
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Let G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G/H be a spherical homogeneous space of G, and let Y′ be a spherical embedding of Y. Let k0 be a subfield of k. Let G0 be a k0-model (k0-form) of G. We show that if G0 is an inner form of a split group and if the subgroup H of G is spherically closed, then Y admits a G0-equivariant k0-model. If we replace the assumption that H is spherically closed by the stronger assumption that H coincides with its normalizer in G, then Y and Y′ admit compatible G0-equivariant k0-models, and these models are unique.
AB - Let G be a connected semisimple group over an algebraically closed field k of characteristic 0. Let Y = G/H be a spherical homogeneous space of G, and let Y′ be a spherical embedding of Y. Let k0 be a subfield of k. Let G0 be a k0-model (k0-form) of G. We show that if G0 is an inner form of a split group and if the subgroup H of G is spherically closed, then Y admits a G0-equivariant k0-model. If we replace the assumption that H is spherically closed by the stronger assumption that H coincides with its normalizer in G, then Y and Y′ admit compatible G0-equivariant k0-models, and these models are unique.
UR - http://www.scopus.com/inward/record.url?scp=85065175175&partnerID=8YFLogxK
U2 - 10.1007/s00031-019-09531-w
DO - 10.1007/s00031-019-09531-w
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AN - SCOPUS:85065175175
SN - 1083-4362
VL - 25
SP - 391
EP - 439
JO - Transformation Groups
JF - Transformation Groups
IS - 2
ER -