Search Results - "Karpenko, Nikita A"

Envelopes and classifying spaces by Karpenko, Nikita A.

“…For a split semisimple algebraic group H with its split maximal torus S , let be the restriction homomorphism of the Chow rings of the classifying spaces of H…”
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Maximal indexes of flag varieties for spin groups by Devyatov, Rostislav A., Karpenko, Nikita A., Merkurjev, Alexander S.

“…We establish the sharp upper bounds on the indexes for most of the twisted flag varieties under the spin groups ${\operatorname {\mathrm {Spin}}(n)}$…”
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Filtrations on the representation ring of an affine algebraic group by Karpenko, Nikita A

“…Abstract Let G be an affine algebraic group over a field. The representation ring $\mathrm{R}(G)$ has three standard filtrations, defining the same topology on…”
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Hyperbolicity of unitary involutions by Karpenko, Nikita A.

“…We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal…”
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Extended Petrov–Semenov’s connections by Karpenko, Nikita A.

“…For a smooth projective quadric X , Alexander Vishik introduced the notion of connections . He discovered connections arising from the splitting pattern of X…”
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Chow ring of generic flag varieties by Karpenko, Nikita A.

“…Let G be a split semisimple algebraic group over a field k and let X be the flag variety (i.e., the variety of Borel subgroups) of G twisted by a generic…”
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On generic flag varieties of Spin(11) and Spin(12) by Karpenko, Nikita A.

“…Let X be the variety of Borel subgroups of a split semisimple algebraic group G over a field, twisted by a generic G -torsor. Conjecturally, the canonical…”
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Chow Filtration on Representation Rings of Algebraic Groups by Karpenko, Nikita A, Merkurjev, Alexander S

“…Abstract We introduce and study a filtration on the representation ring $R(G)$ of an affine algebraic group $G$ over a field. This filtration, which we call…”
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Essential dimension of finite p-groups by Karpenko, Nikita A., Merkurjev, Alexander S.

“…We prove that the essential dimension and p -dimension of a p -group G over a field F containing a primitive p -th root of unity is equal to the least…”
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ISOTROPY OF ORTHOGONAL INVOLUTIONS by Karpenko, Nikita A., Tignol, Jean-Pierre

“…An orthogonal involution on a central simple algebra becoming isotropic over any splitting field of the algebra, becomes isotropic over a finite odd degree…”
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On the first Witt index of quadratic forms by Karpenko, Nikita A.

“…We prove Hoffmann's conjecture determining the possible values of the first Witt index of anisotropic quadratic forms of any given dimension. The proof makes…”
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On special Clifford groups and their characteristic classes by Karpenko, Nikita A.

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On generic flag varieties for odd spin groups by Karpenko, Nikita A.

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A bound for canonical dimension of the (semi)spinor groups by Karpenko, Nikita A.

“…Using the theory of nonnegative intersections, duality of the Schubert varieties, and a Pieri-type formula for the varieties of maximal, totally isotropic…”
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An ultimate proof of Hoffmann–Totaro’s conjecture by Karpenko, Nikita A.

“…We prove the last open case of the conjecture on the possible values of the first isotropy index of an anisotropic quadratic form over a field. It was…”
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Chow ring of generically twisted varieties of complete flags by Karpenko, Nikita A.

“…Let G be a split simple affine algebraic group of type A or C over a field k, and let E be a standard generic G-torsor over a field extension of k. We compute…”
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On Classifying Spaces of Spin Groups by Karpenko, Nikita A.

“…For a split maximal torus T of a split spin group G = Spin ( n ) over an arbitrary field, we consider the restriction homomorphism of the Chow rings of their…”
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Yagita’s counter-examples and beyond by Baek, Sanghoon, Karpenko, Nikita A.

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On generically split generic flag varieties by Karpenko, Nikita A.

“…Let G be a split semisimple algebraic group over an arbitrary field F, let E be a G‐torsor over F, and let P be a parabolic subgroup of G. The quotient variety…”
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Indexes of generic Grassmannians for spin groups by Karpenko, Nikita A., Merkurjev, Alexander S.

“…Given integers d$d$ and m$m$, satisfying 1⩽m⩽d/2$1\leqslant m\leqslant d/2$, and an arbitrary base field, let Xm$X_m$ be the m$m$th Grassmannian of a generic…”
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