منابع مشابه
Grothendieck Chow-motives of Severi-Brauer varieties
For any central simple algebra, the Grothendieck Chow-motive of the corresponding Severi-Brauer variety is decomposed in a direct sum where each summand is a twisted motive of the Severi-Brauer variety corresponding to the underlying division algebra. It leads to decompositions in other theories (for instance, of K-cohomologies) because of the universal property of the Chow-motives. In the seco...
متن کاملCycles on Severi - Brauer Varieties
For a given sequence of integers (n i) 1 i=1 we consider all the central simple algebras A (over all elds) satisfying the condition ind A i = n i and nd among them an algebra having the biggest torsion in the second Chow group CH 2 of the corresponding Severi-Brauer variety (\biggest" means that it can be mapped epimorphically onto each other). We describe this biggest torsion in a way in gener...
متن کاملIncompressibility of Generalized Severi-brauer Varieties
Let F be an arbitrary field. Let A be a central simple F -algebra. Let G be the algebraic group AutA of automorphisms of A. Let XA be the class of finite direct products of projective G-homogeneous F -varieties (the class XA includes the generalized Severi-Brauer varieties of the algebra A). Let p be a positive prime integer. For any variety in XA, we determine its canonical dimension at p. In ...
متن کاملA Lie algebra method for rational parametrization of Severi–Brauer surfaces
It is well known that a Severi–Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi–Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We give an algorithm using Lie algebra tec...
متن کاملGalois Descent and Severi-brauer Varieties
We say an algebraic object or property over a field k is arithmetic if it becomes trivial or vanishes after finite separable base extension. Since such objects or properties owe their existence to the presence of “arithmetic gaps” in k, i.e., the failure of k to be algebraically closed, we view them as responses to specific arithmetic properties of k, and we study them in order to gain insight ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2008
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-08-09450-1