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THE ESSENTIAL DIMENSION OF A g-DIMENSIONAL COMPLEX ABELIAN VARIETY IS 2g
ESSENTIAL DIMENSION COMPLEX ABELIAN VARIETY IS 2g
2015/9/29
We compute the Buhler-Reichstein essential dimension of a complex abelian variety using Kummer theory.
Essential dimension is a numerical invariant of an algebraic
group G introduced by J. Buhler and the second author to study the
complexity of G-torsors over a eld K. It has since been studied by se...
We prove that the essential dimension of the spinor group
Spinn grows exponentially with n and use this result to show that quadratic forms with trivial discriminant and Hasse-Witt invariant are more...
ESSENTIAL DIMENSION OF MODULI OF CURVES AND OTHER ALGEBRAIC STACKS (WITH AN APPENDIX BY NAJMUDDIN FAKHRUDDIN)
ESSENTIAL DIMENSION OTHER ALGEBRAIC STACKS
2015/9/29
In this paper we consider questions of the following type.
Let k be a base eld and K=k be a eld extension. Given a geometric
object X over a eld K (e.g. a smooth curve of genus g) what is the
le...
ESSENTIAL DIMENSION OF ABELIAN VARIETIES OVER NUMBER FIELDS
ESSENTIAL DIMENSION OVER NUMBER FIELDS
2015/9/29
We affirmatively answer a conjecture in the preprint “Essential
dimension and algebraic stacks,” proving that the essential dimension of an
abelian variety over a number field is inʂ...
Essential dimension of simple algebras in positive characteristic
Essential dimension simple algebras positive characteristic
2011/2/24
Let p be a prime integer, 1 ≤ s ≤ r integers, F a field of characteristic p.
On the essential dimension of unipotent algebraic groups
essential dimension unipotent algebraic groups
2011/1/21
We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field k which is finitely generated over a perfect field, a s...