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    Title   l  Algebraic cobordism theory attached to algebraic equivalence
    Journal   l  Journal of K-theory 
    Year   l  2013
    Vol   l  11
    No   l  1
    Pages   l  73-112
    Author   l  Krishna, Amalendu; Park, Jinhyun
    DownLoad    l
Based on the algebraic cobordism theory of Levine and Morel, we develop a theory of algebraic cobordism modulo algebraic equivalence.

We prove that this theory can reproduce Chow groups modulo algebraic equivalence and the semi-topological K-0-groups. We also show that with finite coefficients, this theory agrees with the algebraic cobordism theory.

We compute our cobordism theory for some low dimensional varieties. The results on infinite generation of some Griffiths groups by Clemens and on smash-nilpotence by Voevodsky and Voisin are also lifted and reinterpreted in terms of this cobordism theory.

Keyword

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2016 Anandam Banerjee, Jinhyun Park. On numerical equivalence for algebraic cobordism, J. Pure Appl. Algebra, 220(1):435-464
2015 Amalendu Krishna, Jinhyun Park. Semitopologization in motivic homotopy theory and applications, Algebraic & Geometric Topology, 15(2):823-861
2015 Amalendu Krishna, Jinhyun Park. DGA-structure on additive higher Chow groups, Int. Math. Res. Not., 2015(1):1-54
2015 Junehyuk Jung. Number of nodal domains and singular points of eigenfunctions of negatively curved surfaces with an isometric involution, J. Differential Geom., Vol. accepted
2015 Junehyuk. On the sparsity of positive-definite automorphic forms within a family, J. Anal. Math., Vol. accepted
2014 Sijong Kwak, Kangjin Han. Sharp bounds for higher linear syzygies and classifications of projective varieties, Math. Ann., Vol. DOI 10.1007/s00208-014-1084-9
2014 Sijong Kwak, Jaeman Ahn. On Syzygies, degree, and geometric properties of projective schemes with property N_{3,p}., J Pure and Applied Algebra(JPAA),
2014 Cheol-Hyun Cho. Orbifold Morse–Smale–Witten complexes, International Journal of Mathematics, 25(5):Doi:10.1142
2014 Cheol-Hyun Cho, Kwokwai Chan, Siu-Cheong Lau, Hsian-Hua Tseng. Lagrangian Floer Superpotentials and Crepant Resolutions for Toric Orbifolds, Communications in mathematical physics, DOI 10.1007/s00220-014-1
2013 Krishna, Amalendu; Park, Jinhyun. Algebraic cobordism theory attached to algebraic equivalence, Journal of K-theory, 11(1):73-112
2012 Krishna, Amalendu, Park, Jinhyun. Mixed motives over k[t]/(t^{m+1}), Journal of the Institute of Mathematics of Jussieu, 11(3):611-657
2012 rishna, Amalendu; Park, Jinhyun. Moving lemma for additive higher Chow groups, Algebra & Number Theory, Algebra & Number Theory, 6(2):293-326
2014 Sang June Lee. On constant-multiple-free sets contained in random sets of integers, Ars Combinatoria,
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2013 Cho, Cheol-Hyun1. On the counting of holomorphic discs in toric Fano manifolds, Advances in Geometry, Vol. DOI: 10.1515/advgeom-2012-0041
2012 Antei M.. Extension of finite solvable torsors over a curve, Manuscripta Mathematica, Vol. doi: 10.1007/s00229-012-0535-4
2012 Antei M., Mehta V. B.. On the Grothendieck-Lefschetz theorem for a family of varieties, Bulletin des Sciences Mathématiques, 136(4):423 - 431
2011 Marco Antei and Vikram B. Mehta. Vector bundles over normal varieties trivialized by finite morphisms DOI: 10.1007/s00013-011-0327-1, Archiv der Mathematik, 97(6):523-527
2011 Antei M. The fundamental group scheme of a non reduced scheme, Bulletin des Sciences Mathématiques, 135(5):531-539
2011 Jung Hee Cheon · Jin Hong · Minkyu Kim. Accelerating Pollard’s Rho Algorithm on Finite Fields, Journal of Cryptology,
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