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Essential dimension of simple algebras with involutions
Let be integers with and \cat{Alg}_{n,m} the class
of central simple algebras of degree and exponent dividing . In this
paper, we find new, improved upper bounds for the essential dimension and
2-dimension of \cat{Alg}_{n,2}. In particular, we show that
\ed_{2}(\cat{Alg}_{16,2})=24 over a field of characteristic different
from 2.Comment: Sections 1 and 3 are rewritte
Essential dimension of simple algebras in positive characteristic
Let be a prime integer, integers, a field of
characteristic . Let \cat{Dec}_{p^r} denote the class of the tensor
product of -symbols and \cat{Alg}_{p^r,p^s} denote the class of
central simple algebras of degree and exponent dividing . For any
integers , we find a lower bound for the essential -dimension of
\cat{Alg}_{p^r,p^s}. Furthermore, we compute upper bounds for
\cat{Dec}_{p^r} and \cat{Alg}_{8,2} over and ,
respectively. As a result, we show
\ed_{2}(\cat{Alg}_{4,2})=\ed(\cat{Alg}_{4,2})=\ed_{2}(\gGL_{4}/\gmu_{2})=\ed(\gGL_{4}/\gmu_{2})=3
and 3\leq \ed(\cat{Alg}_{8,2})=\ed(\gGL_{8}/\gmu_{2})\leq 10 over a field of
characteristic 2.Comment: Any comments are welcom
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