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Applications of AtiyahHirzebruch spectral sequence for motivic cobordism
 Department of Mathematics, Faculty of Education, Ibaraki University
"... Abstract. We study applications of AtiyahHirzebruch spectral sequences for motivic cobordisms found by Hopkins and Morel. 1. ..."
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Abstract. We study applications of AtiyahHirzebruch spectral sequences for motivic cobordisms found by Hopkins and Morel. 1.
NONHOMEOMORPHIC CONJUGATE COMPLEX VARIETIES
, 2007
"... We present a method to produce examples of nonhomeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs. ..."
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Cited by 13 (4 self)
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We present a method to produce examples of nonhomeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs.
Some aspects of the Hodge conjecture
 Japanese Journal of Mathematics
, 2007
"... 0.1 Hodge theory............................... 2 0.2 Hodge classes and the Hodge conjecture................ 4 0.3 Lefschetz theorem on (1, 1)classes................... 5 ..."
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Cited by 13 (5 self)
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0.1 Hodge theory............................... 2 0.2 Hodge classes and the Hodge conjecture................ 4 0.3 Lefschetz theorem on (1, 1)classes................... 5
SCHUBERT CALCULUS FOR ALGEBRAIC COBORDISM
, 2009
"... We give an explicit formula for the pushforward morphism in algebraic cobordism for projective line fibrations. Using this formula, we establish a Schubert calculus for BottSamelson resolutions in the algebraic cobordism ring of a complete flag variety G/B. ..."
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We give an explicit formula for the pushforward morphism in algebraic cobordism for projective line fibrations. Using this formula, we establish a Schubert calculus for BottSamelson resolutions in the algebraic cobordism ring of a complete flag variety G/B.
Transfers of Chern classes in BPcohomology and Chow rings
 Trans. Amer. Math. Soc
"... Abstract. The BP ∗module structure of BP ∗ (BG) for extraspecial 2groups is studied using transfer and Chern classes. These give rise to ptorsion elements in the kernel of the cycle map from the Chow ring to ordinary cohomology first obtained by Totaro. 1. ..."
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Abstract. The BP ∗module structure of BP ∗ (BG) for extraspecial 2groups is studied using transfer and Chern classes. These give rise to ptorsion elements in the kernel of the cycle map from the Chow ring to ordinary cohomology first obtained by Totaro. 1.
THE MORPHIC ABELJACOBI MAP
"... Abstract. The morphic AbelJacobi map is the analogue of the classical AbelJacobi map one obtains by using Lawson and morphic (co)homology in place of the usual singular (co)homology. It thus gives a map from the group of rcycles on a complex variety that are algebraically equivalent to zero to a ..."
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Abstract. The morphic AbelJacobi map is the analogue of the classical AbelJacobi map one obtains by using Lawson and morphic (co)homology in place of the usual singular (co)homology. It thus gives a map from the group of rcycles on a complex variety that are algebraically equivalent to zero to a certain “Jacobian ” built from the Lawson homology groups viewed as inductive limits of mixed Hodge structures. In this paper, we define the morphic AbelJacobi map, establish its foundational properties, and then apply these results to the study of algebraic cycles. In particular, we show the classical AbelJacobi map (when restricted to cycles algebraically equivalent to zero) factors through the morphic version, and show that the morphic version detects cycles that cannot be detected by its classical counterpart — that is, we give examples of cycles in the kernel of the classical AbelJacobi map that are not in the kernel of the morphic one. We also investigate the behavior of the morphic AbelJacobi map on the torsion subgroup of the Chow group of cycles algebraically equivalent to zero modulo
ALGEBRAIC COBORDISM OF SIMPLY CONNECTED LIE GROUPS
"... Abstract. Let GC be the algebraic group over C corresponding a simply connected Lie group G. The algebraic cobordism Ω(GC) defined by Levine and Morel is showed isomorphic to MU ∗subalgebra of MU ∗ (G) with some modulous and is computed explicitely. 1. ..."
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Abstract. Let GC be the algebraic group over C corresponding a simply connected Lie group G. The algebraic cobordism Ω(GC) defined by Levine and Morel is showed isomorphic to MU ∗subalgebra of MU ∗ (G) with some modulous and is computed explicitely. 1.
BrownPeterson spectra in stable A 1 homotopy theory
"... We characterize ring spectra morphism from the algebraic cobordism spectrum MGL to an oriented spectrum E (in the sense of Morel [Mo]) via formal group laws on the ”topological” subring E ∗ = ⊕iE 2i,i of E ∗ ∗. This result is then used to construct BPspectra in essentially the same way Quillen ([Q ..."
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We characterize ring spectra morphism from the algebraic cobordism spectrum MGL to an oriented spectrum E (in the sense of Morel [Mo]) via formal group laws on the ”topological” subring E ∗ = ⊕iE 2i,i of E ∗ ∗. This result is then used to construct BPspectra in essentially the same way Quillen ([Q1]) did for the complexoriented topological case. 1
Equivariant Cobordism of Schemes
 DOCUMENTA MATH.
, 2012
"... Let k be a field of characteristic zero. For a linear algebraic group G over k acting on a scheme X, we define the equivariant algebraic cobordism of X and establish its basic properties. We explicitly describe the relation of equivariant cobordism with equivariant Chow groups, Kgroups and complex ..."
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Let k be a field of characteristic zero. For a linear algebraic group G over k acting on a scheme X, we define the equivariant algebraic cobordism of X and establish its basic properties. We explicitly describe the relation of equivariant cobordism with equivariant Chow groups, Kgroups and complex cobordism. We show that the rational equivariant cobordism of a Gscheme can be expressed as the Weyl group invariants of the equivariant cobordism for the action of a maximal torus of G. As applications, we show that the rational algebraic cobordism of the classifying space of a complex linear algebraic group is isomorphic to its complex cobordism.