Incompressibility of Products of Pseudo-homogeneous Varieties

2016 ◽  
Vol 59 (4) ◽  
pp. 824-833 ◽  
Author(s):  
Nikita A. Karpenko
Keyword(s):  
Galois Cohomology ◽  
Arbitrary Degree ◽  
Special Cases ◽  
Projective Homogeneous Varieties ◽  
Homogeneous Varieties

AbstractWe show that the conjectural criterion of p-incompressibility for products of projective homogeneous varieties in terms of the factors, previously known in a few special cases only, holds in general. Actually, the proof goes through for a wider class of varieties, including the norm varieties associated with symbols in Galois cohomology of arbitrary degree.

Motivic decomposition of isotropic projective homogeneous varieties

2005 ◽  
Vol 126 (1) ◽  
pp. 137-159 ◽  
Author(s):  
Vladimir Chernousov ◽  
Stefan Gille ◽  
Alexander Merkurjev
Keyword(s):  
Projective Homogeneous Varieties ◽  
Homogeneous Varieties

Algebraic Cobordism and Projective Homogeneous Varieties

2016 ◽  
Vol 13 (1) ◽  
pp. 215-265
Author(s):  
Stefan Gille ◽  
Marc Levine ◽  
Ivan Panin ◽  
Alexander Vishik
Keyword(s):  
Projective Homogeneous Varieties ◽  
Algebraic Cobordism ◽  
Homogeneous Varieties

Generically split projective homogeneous varieties. II

2012 ◽  
Vol 10 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Victor Petrov ◽  
Nikita Semenov
Keyword(s):  
Complete Classification ◽  
Previous Article ◽  
Base Field ◽  
Projective Homogeneous Varieties ◽  
Homogeneous Varieties

AbstractThis article gives a complete classification of generically split projective homogeneous varieties. This project was begun in our previous article [PS10], but here we remove all restrictions on the characteristic of the base field, give a new uniform proof that works in all cases and in particular includes the case PGO2n+ which was missing in [PS10].

scholarly journals Exceptional collections of line bundles on projective homogeneous varieties

2013 ◽  
Vol 236 ◽  
pp. 111-130 ◽  
Author(s):  
Alexey Ananyevskiy ◽  
Asher Auel ◽  
Skip Garibaldi ◽  
Kirill Zainoulline
Keyword(s):  
Line Bundles ◽  
Projective Homogeneous Varieties ◽  
Homogeneous Varieties

Rational maps between quasilinear hypersurfaces

2012 ◽  
Vol 149 (3) ◽  
pp. 333-355 ◽  
Author(s):  
Stephen Scully
Keyword(s):  
Rational Maps ◽  
Base Field ◽  
Geometric Methods ◽  
Alternative Approach ◽  
Projective Homogeneous Varieties ◽  
Homogeneous Varieties

AbstractWe prove analogues of several well-known results concerning rational maps between quadrics for the class of so-called quasilinear p-hypersurfaces. These hypersurfaces are nowhere smooth over the base field, so many of the geometric methods which have been successfully applied to the study of projective homogeneous varieties over fields cannot be used. We are therefore forced to take an alternative approach, which is partly facilitated by the appearance of several non-traditional features in the study of these objects from an algebraic perspective. Our main results were previously known for the class of quasilinear quadrics. We provide new proofs here, because the original proofs do not immediately generalise for quasilinear hypersurfaces of higher degree.

scholarly journals Generically split projective homogeneous varieties

2010 ◽  
Vol 152 (1) ◽  
pp. 155-173 ◽  
Author(s):  
Viktor Petrov ◽  
Nikita Semenov
Keyword(s):  
Projective Homogeneous Varieties ◽  
Homogeneous Varieties
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