Titlebook: Value Functions on Simple Algebras, and Associated Graded Rings; Jean-Pierre Tignol,Adrian R. Wadsworth Book 2015 Springer International P

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Brauer Groups,ain analogues of the general results on the Brauer group of fields. Graded fields have a special structure however, since the degree?0 component is a canonically-defined subfield. This structure is reflected in a canonical filtration of the Brauer group of graded fields. The second section aims to r

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Division Algebras over Henselian Fields,ng results for graded division algebras, then lifting back from . to .. This is facilitated by results in §. on existence and uniqueness of lifts of tame subalgebras from . to .. In §., we describe four fundamental canonical (up to conjugacy) subalgebras of . that reflect its valuative structure. Th

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Autobiography

Indecomposable Division Algebras,e give examples of indecomposable algebras, emphasizing constructions that use valuation theory. In light of the primary decomposition, we restrict attention to division algebras of prime power degree. Indecomposable algebras of exponent?.. or higher are relatively easy to construct as “.-th roots”

Brochure

Computation of ,,(,),. This group? ..(.) is a subtle invariant of .. that has been of longstanding interest to those working with central simple algebras, algebraic groups, and .-theory. Since .. is a Brauer class invariant, it suffices to compute .. for division algebras. We prove here nearly all the known formulas for

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The Essential Dimension of Central Simple Algebras,eters needed to define it. For a prime number ., the essential .-dimension is a variation of essential dimension that takes into account simplifications in structure that can occur after field extensions of degree prime to .. In §. we define the basic notions of essential dimension and essential .-d

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Book 2015search over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur‘s construction of non crossed products and Platonov‘s solution of the Tannaka-Artin problem..This study is particularly timely because it approaches the su

Ingredient

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Computation of ,,(,), ..(.) for . a tame central division algebra over a Henselian field. We do this by first obtaining in §. formulas for .. in the graded setting, where calculations are substantially easier and more transparent. We then recover in §. the corresponding formulas in the valued setting by proving in Th.?. that . for .=.(.) Henselian and . tame over ..