INVARIANTS, TORSION INDICES AND ORIENTED COHOMOLOGY OF COMPLETE FLAGS

被引:0
|
作者
Calmes, Baptiste [1 ]
Petrov, Viktor [2 ]
Zainoulline, Kirill [3 ]
机构
[1] Univ Artois, Fac Sci Jean Perrin, Lab Math Lens, F-62307 Lens, France
[2] VA Steklov Math Inst, St Petersburg 191023, Russia
[3] Univ Ottawa, Dept Math & Stat, Ottawa, ON KIN 6N5, Canada
基金
加拿大自然科学与工程研究理事会; 英国工程与自然科学研究理事会;
关键词
SCHUBERT CALCULUS;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a split semisimple linear algebraic group over a field and let T be a split maximal torus of G. Let h be an oriented cohomology (algebraic cobordism, connective K-theory, Chow groups, Grothendieck's K-0, etc.) with formal group law F. We construct a ring from F and the characters of T, that we call a formal group ring, and we define a characteristic ring morphism c from this formal group ring to h (G/B) where G/B is the variety of Borel subgroups of G. Our main result says that when the torsion index of G is inverted, c is surjective and its kernel is generated by elements invariant under the Weyl group of G. As an application, we provide an algorithm to compute the ring structure of h (G/B) and to describe the classes of desingularized Schubert varieties and their products.
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页码:405 / 448
页数:44
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