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Volume Contents
K-Theory Contents of Volume 22 相似文献2.
Oleg T. Izhboldin 《manuscripta mathematica》2000,102(1):41-52
Let F be a field of characteristic ≠2 and φ be a quadratic form over F. By X
φ we denote the projective variety given by the equation φ=0. For each positive even integer d≥8 (except for d=12) we construct a field F and a pair φ, ψ of anisotropic d-dimensional forms over F such that the Chow motives of X
φ and X
ψ coincide but . For a pair of anisotropic (2
n
-1)-dimensional quadrics X and Y, we prove that existence of a rational morphism Y→X is equivalent to existence of a rational morphism Y→X.
Received: 27 September 1999 / Revised version: 27 December 1999 相似文献
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Let F be a field of characteristic different from 2 and let ø be an anisotropic 8-dimensional quadratic form over F with trivial deter-minant. We study the remaining open cases in the problem of describing the quadratic forms ψ such that ø becomes isotropic over the function field (ψ). 相似文献
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Oleg T. Izhboldin 《K-Theory》2001,22(3):199-229
Let F be a field of characteristic different from 2 and be a quadratic form over F. Let X be an arbitrary projective homogeneous generic splitting variety of . For example, we can take X to be equal to the variety X,m of totally isotropic m-dimensional subspaces of V, where V is the quadratic space corresponding to and <
dim V. In this paper, we study the groups CH2(X) and H3(F(X)/F) = ker(H
3(F) H
3(F(X))). One of the main results of this paper claims that the group Tors CH2(X) is always zero or isomorphic to
. In many cases we prove that Tors CH2(X) = 0 and compute the group H
3(F(X)/F) completely. As an application of the main results, we give a criterion of motivic equivalence of eight-dimensional forms except for the case where the Schur indices of their Clifford algebras equal 4. 相似文献
5.
We construct a 6-dimensional anisotropic quadratic form and a 4-dimensional quadratic form over some fieldF such that becomes isotropic over the function field but every proper subform of is still anisotropic over . It is an example of non-standard isotropy with respect to some standard conditions of isotropy for 6-dimensional forms over function fields of quadrics, known previously. Besides of that, we produce an 8-dimensional quadratic form with trivial determinant such that the index of the Clifford invariant of is 4 but can not be represented as a sum of two 4-dimensional forms with trivial determinants. Using this, we find a 14-dimensional quadratic form with trivial discriminant and Clifford invariant, which is not similar to a difference of two 3-fold Pfister forms. The proofs are based on computations of the topological filtration on the Grothendieck group of certain projective homogeneous varieties. To do these computations, we develop several methods, covering a wide class of varieties and being, to our mind, of independent interest. Received November 11, 1997; in final form June 24, 1999 / Published online May 8, 2000 相似文献
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A field extension L / F is called excellent if, for any quadratic form over F, the anisotropic part (L)an of over L is defined over F; L / F is called universally excellent if L E / E is excellent for any field extension E / F. We study the excellence property for a generic splitting field of a central simple F-algebra. In particular, we show that it is universally excellent if and only if the Schur index of the algebra is not divisible by 4. We begin by studying the torsion in the second Chow group of products of Severi–Brauer varieties and its relationship with the relative Galois cohomology group H3(L / F) for a generic (common) splitting field L of the corresponding central simple F-algebras. 相似文献
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Blyuss Konstantin B. Al Basir Fahad Tsygankova Victoria A. Biliavska Liudmyla O. Iutynska Galyna O. Kyrychko Serhii N. Dziuba Serhii V. Tsyliuryk Olexandr I. Izhboldin Olexandr O. 《Ricerche di matematica》2020,69(2):437-455
Ricerche di Matematica - A major challenge to successful crop production comes from viral diseases of plants that cause significant crop losses, threatening global food security and the livelihoods... 相似文献
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V. L. Auslender A. A. Bryazgin L. A. Voronin V. A. Polyakov V. P. Grodetskiy I. K. Izhboldin O. M. Mirsaetov A. M. Petrov Yu. T. Obidin V. N. Ponomaryov 《Radiation Physics and Chemistry》1998,52(1-6):459-463
Last years most of the developed countries are using radiation method based on electron accelerators for sterilization of medical goods as mostly safe and ecologically pure from all known methods. The report describes in details the automated installation for sterilization of single-use syringes working in the city of Izhevsk, Russia. The syringes are irradiated from two sides inside the packs containing 250 units each. The packs are automatically turned on the inclined part of the conveyor under influence of their own weight. The syringes are posed vertically along the beam fall. The ration of maximal absorbed dose to minimal is 1.4. The productive rate of installation is no less 100 000 syringes per hour. The installation is based on the linear pulse electron accelerator ILU-6. It is the single cavity machine with electron energy up to 2.5 MeV and average beam power up to 20 kW. The pulse nature of the current and automatic control system permit to vary the absorbed dose in great range. The electron energy, beam current, pulse repetition rate, beam position in the extracted window and transportation of the treated products are computer controlled. 相似文献
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