DIEUDONNÉ'S CONJECTURE ON THE STRUCTURE OF UNITARY GROUPS OVER A DIVISION RING, AND HERMITIAN<i>K</i>-THEORY

Платонов, В. П.; Yanchevskii, V. I.

doi:10.1070/im1985v025n03abeh001308

Cited by 17 publications

(14 citation statements)

References 6 publications

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“…The nondegeneracy assures that the image of Cd contains all /th roots of unity and. as noted in §2, that FD/Ff has the form H x H. □ The fact that pi Q F was noted in the Henselian case in [PY,Proposition 5 This fact may explain why totally ramified division algebras were not studied many years earlier.…”

Section: Proof (Ii)=>(i) Is Immediate From Examples 24(b) and (D)mentioning

confidence: 99%

Totally Ramified Valuations on Finite-Dimensional Division Algebras

Tignol¹,

Wadsworth²

1987

Transactions of the American Mathematical Society

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Section: Proof (Ii)=>(i) Is Immediate From Examples 24(b) and (D)mentioning

confidence: 99%

Totally Ramified Valuations on Finite-Dimensional Division Algebras

Tignol¹,

Wadsworth²

1987

Transactions of the American Mathematical Society

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“…Here we concentrate on involutions of the first kind, i.e., We will prove that there is a stability theorem for GU D similar to one in Corollary 3.7. The first part of the following theorem was first proved by Platonov and Yanchevskii [16]. …”

Section: On the Unitary Settingmentioning

confidence: 94%

SK1-like Functors for Division Algebras

Hazrat

2001

Journal of Algebra

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We investigate the group valued functor G D = D * /F * D where D is a division algebra with center F and D the commutator subgroup of D * . We show that G has the most important functorial properties of the reduced Whitehead group SK 1 . We then establish a fundamental connection between this group, its residue version, and relative value group when D is a Henselian division algebra. The structure of G D turns out to carry significant information about the arithmetic of D. Along these lines, we employ G D to compute the group SK 1 D . As an application, we obtain theorems of reduced K-theory which require heavy machinery, as simple examples of our method.

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“…The inertial case of the preceding proposition is already contained in essence in a paper of Platonov and Yanchevskiϊ: see the proof of Proposition 5.9 of [17]. (To avoid misunderstanding the statement of this proposition, the reader should keep in mind that Platonov and Yanchevskiϊ assume throughout §5 of [17] that the given involution is of symplectic type.…”

Section: Deg(d)=deg(d)[z(d):f]mentioning

confidence: 99%

“…(To avoid misunderstanding the statement of this proposition, the reader should keep in mind that Platonov and Yanchevskiϊ assume throughout §5 of [17] that the given involution is of symplectic type. )…”

Section: Deg(d)=deg(d)[z(d):f]mentioning

confidence: 99%