On the Chow groups of quadratic Grassmannians.
Vishik, A. (2005)
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Vishik, A. (2005)
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Brosnan, Patrick (2003)
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Nikita Karpenko (2013)
Open Mathematics
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We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular,...
Arason, Jón Kr. (2001)
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Roberts, Brooks (2001)
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Brendan Hassett, Yuri Tschinkel (2014)
Open Mathematics
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We classify quartic del Pezzo surface fibrations over the projective line via numerical invariants, giving explicit examples for small values of the invariants. For generic such fibrations, we describe explicitly the geometry of spaces of sections to the fibration, and mappings to the intermediate Jacobian of the total space. We exhibit examples where these are birational, which has applications to arithmetic questions, especially over finite fields.
Knus, Max-Albert, Villa, Oliver (2001)
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Vishik, A., Zainoulline, K. (2008)
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Hoffmann, Detlev W. (2010)
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Hoffmann, Detlev W. (2001)
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Baeza, Ricardo (2001)
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Weinstein, Jared (2010)
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