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15
Algebraic cobordisms of a Pfister quadric
, 2005
"... The aim of this paper is to compute algebraic cobordisms of Pfister quadric Qα. We present two different approaches to this problem. The first one uses the motivic spectrum MGL (constructed by V.Voevodsky in [19]), and is reduced to the computation of MGL 2∗, ∗ (Qα), and the second one uses the ..."
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The aim of this paper is to compute algebraic cobordisms of Pfister quadric Qα. We present two different approaches to this problem. The first one uses the motivic spectrum MGL (constructed by V.Voevodsky in [19]), and is reduced to the computation of MGL 2∗, ∗ (Qα), and the second one uses the
On the cohomology and the Chow ring of the classifying space PGLp
"... Abstract. We investigate the integral cohomology ring and the Chow ring of the classifying space of the complex projective linear group PGLp, when p is an odd prime. In particular, we determine their additive structures completely, and we reduce the problem of determining their multiplicative struct ..."
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Abstract. We investigate the integral cohomology ring and the Chow ring of the classifying space of the complex projective linear group PGLp, when p is an odd prime. In particular, we determine their additive structures completely, and we reduce the problem of determining their multiplicative structures to a problem in invariant theory. Contents
The BrownPeterson cohomology of the classifying spaces of the projective unitary groups PU(p) and exceptional Lie group Trans
 of A.M.S
"... Abstract. For a fixed prime p, we compute the BrownPeterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP ∗ (BPU(p)) and K(n) ∗ (BPU(p)) are even dimensionally generated. 1. ..."
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Abstract. For a fixed prime p, we compute the BrownPeterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP ∗ (BPU(p)) and K(n) ∗ (BPU(p)) are even dimensionally generated. 1.
ALGEBRAIC COBORDISM OF CLASSIFYING SPACES
, 907
"... Abstract. We define algebraic cobordism of classifying spaces, Ω ∗ (BG) and Gequivariant algebraic cobordism Ω ∗ G (−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F j (Ω∗(−)), which are required for the definition to work. We s ..."
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Abstract. We define algebraic cobordism of classifying spaces, Ω ∗ (BG) and Gequivariant algebraic cobordism Ω ∗ G (−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F j (Ω∗(−)), which are required for the definition to work. We show that Gequivariant cobordism satisfies the localization exact sequence. We calculate Ω ∗ (BG) for algebraic groups over the complex numbers corresponding to classical Lie groups GL(n), SL(n), Sp(n), O(n) and SO(2n+1). We also calculate Ω ∗ (BG) when G is a finite abelian group. A finite nonabelian group for which we calculate Ω ∗ (BG) is the quaternion group of order 8. In all the above cases we check that Ω ∗ (BG) is isomorphic to MU ∗ (BG). 1.
Motivic Brown–Peterson invariants of the rationals
"... Let BPhni, 0 n 1, denote the family of motivic truncated Brown–Peterson spectra over Q. We employ a “localtoglobal ” philosophy in order to compute the bigraded homotopy groups of BPhni. Along the way, we produce a computation of the homotopy groups of BPhni over Q2, prove a motivic Hasse principl ..."
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Let BPhni, 0 n 1, denote the family of motivic truncated Brown–Peterson spectra over Q. We employ a “localtoglobal ” philosophy in order to compute the bigraded homotopy groups of BPhni. Along the way, we produce a computation of the homotopy groups of BPhni over Q2, prove a motivic Hasse principle for the spectra BPhni, and reprove several classical and recent theorems about the K –theory of particular fields in a streamlined fashion. We also compute the bigraded homotopy groups of the 2–complete algebraic cobordism spectrum MGL over Q. 55T15; 19D50, 19E15 1
Coniveau filtration of cohomology of groups
 Department of Mathematics, Faculty of Science, Ryukyu University
"... Abstract. We consider natural ltrations of H(BG;Z=p) for a compact Lie group G, such that (Fi) Fi−1 for the Bockstein operation. An example of such ltrations is dened by i = 2n − m for elements in the image from the motivic cohomology Hm;n(BG;Z=p). For some cases e.g., On, PGLp, we see that this l ..."
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Abstract. We consider natural ltrations of H(BG;Z=p) for a compact Lie group G, such that (Fi) Fi−1 for the Bockstein operation. An example of such ltrations is dened by i = 2n − m for elements in the image from the motivic cohomology Hm;n(BG;Z=p). For some cases e.g., On, PGLp, we see that this ltration coincides the coniveau ltration dened by Grothendieck, 1.
Note on the mod p motivic cohomology of algebraic groups hopf.math.purdue.edu/cgibin/generate?/Yagita/motsplitGpreprint
, 2008
"... Abstract. Let Gk be a split reductive group over a eld k of ch(k) = 0 corresponding to a compact Lie group G. Let H; 0 (Gk;Z=p) ..."
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Abstract. Let Gk be a split reductive group over a eld k of ch(k) = 0 corresponding to a compact Lie group G. Let H; 0 (Gk;Z=p)
THE IMAGE OF THE MAP FROM GROUP COHOMOLOGY TO GALOIS COHOMOLOGY
"... We study the image of the natural map from group cohomology to Galois cohomology by using motivic cohomology of classifying spaces. ..."
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We study the image of the natural map from group cohomology to Galois cohomology by using motivic cohomology of classifying spaces.
NOTE ON THE FILTRATIONS OF THE KTHEORY
"... Abstract. Let X be a (colimit of) smooth algebraic variety over a subfield of C. Let K0 alg (X) (resp. K0 top (X(C))) be the algebraic (resp. topological) Ktheory of k (resp. complex) vector bundles over X ( resp. X(C))). When K0 alg (X) ∼ = K0 top (X(C)), we study the differences of its three (g ..."
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Abstract. Let X be a (colimit of) smooth algebraic variety over a subfield of C. Let K0 alg (X) (resp. K0 top (X(C))) be the algebraic (resp. topological) Ktheory of k (resp. complex) vector bundles over X ( resp. X(C))). When K0 alg (X) ∼ = K0 top (X(C)), we study the differences of its three (gamma, geometrical and topological) filtrations. In particular, we consider the cases X = BG for an algebraically closed field k, and X = Gk/Tk the twisted form of flag varieties G/T for nonalgebraically closed field k. 1.
CHERN SUBRINGS
, 810
"... Abstract. Let p be an odd prime. We show that for a simplyconnected semisimple complex linear algebraic group, if its integral homology has ptorsion, the Chern classes do not generate the Chow ring of its classifying space. 1. ..."
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Abstract. Let p be an odd prime. We show that for a simplyconnected semisimple complex linear algebraic group, if its integral homology has ptorsion, the Chern classes do not generate the Chow ring of its classifying space. 1.