Essential dimension
نویسندگان
چکیده
منابع مشابه
Essential dimension
Informally speaking, the essential dimension of an algebraic object is the minimal number of independent parameters one needs to define it. This notion was initially introduced in the context where the objects in question are finite field extensions [BuR97]. Essential dimension has since been investigated in several broader contexts, by a range of techniques, and has been found to have interest...
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The essential dimension is a numerical invariant of an algebraic group G which may be thought of as a measure of complexity of G-torsors over fields. A recent theorem of N. Karpenko and A. Merkurjev gives a simple formula for the essential dimension of a finite p-group. We obtain similar formulas for the essential p-dimension of a broad class of groups, which includes all algebraic tori.
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The well-known fiber dimension theorem in algebraic geometry says that for every morphism f : X → Y of integral schemes of finite type, the dimension of every fiber of f is at least dimX−dimY . This has recently been generalized by P. Brosnan, Z. Reichstein and A. Vistoli to certain morphisms of algebraic stacks f : X → Y , where the usual dimension is replaced by essential dimension. We will p...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 2016
ISSN: 0273-0979,1088-9485
DOI: 10.1090/bull/1564