• 제목/요약/키워드: Corestriction

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CORESTRICTION MAP ON BRAUER SUBGROUPS

  • CHOI, EUN-MI
    • 대한수학회논문집
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    • 제20권1호
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    • pp.35-49
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    • 2005
  • For an extension field K of k, a restriction homomorphism on Brauer k-group B(k) maps Brauer k-algebras to Brauer K- algebras by tensor product. A purpose of this work is to study the restriction map that sends radical (Schur) k-algebras to radical (Schur) K-algebras. And we ask an analogous question with respect to corestriction map on Brauer group B(K) that whether the corestriction map sends radical K-algebras to radical k-algebras.

THE INDEX OF THE CORESTRICTION OF A VALUED DIVISION ALGEBRA

  • Hwang, Yoon-Sung
    • 대한수학회지
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    • 제34권2호
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    • pp.279-284
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    • 1997
  • Let L/F be a finite separable extension of Henselian valued fields with same residue fields $\overline{L} = \overline{F}$. Let D be an inertially split division algebra over L, and let $^cD$ be the underlying division algebra of the corestriction $cor_{L/F} (D)$ of D. We show that the index $ind(^cD) of ^cD$ divides $[Z(\overline{D}) : Z(\overline {^cD})] \cdot ind(D), where Z(\overline{D})$ is the center of the residue division ring $\overline{D}$.

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COHOMOLOGY OF GROUPS AND TRANSFER THEOREM

  • Park, Eun-Mi
    • 대한수학회지
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    • 제34권2호
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    • pp.383-393
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    • 1997
  • In this paper, we study the dependence of corestriction (or transfer) map on the choice of transversals. We also study transfer theorems with respect to some commutative subgroups.

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ON TATE-SHAFAREVICH GROUPS OVER CYCLIC EXTENSIONS

  • Yu, Ho-Seog
    • 호남수학학술지
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    • 제32권1호
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    • pp.45-51
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    • 2010
  • Let A be an abelian variety defined over a number field K and let L be a cyclic extension of K with Galois group G = <${\sigma}$> of order n. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and of A over L. Assume III(A/L) is finite. Let M(x) be a companion matrix of 1+x+${\cdots}$+$x^{n-1}$ and let $A^x$ be the twist of $A^{n-1}$ defined by $f^{-1}{\circ}f^{\sigma}$ = M(x) where $f:A^{n-1}{\rightarrow}A^x$ is an isomorphism defined over L. In this paper we compute [III(A/K)][III($A^x$/K)]/[III(A/L)] in terms of cohomology, where [X] is the order of an finite abelian group X.