Algebraic Cobordism
نویسنده
چکیده
Together with F. Morel, we have constructed in [6, 7, 8] a theory of algebraic cobordism, an algebro-geometric version of the topological theory of complex cobordism. In this paper, we give a survey of the construction and main results of this theory; in the final section, we propose a candidate for a theory of higher algebraic cobordism, which hopefully agrees with the cohomology theory represented by the P-spectrum MGL in the Morel-Voevodsky stable homotopy category. 2000 Mathematics Subject Classification: 19E15, 14C99, 14C25.
منابع مشابه
Algebraic Cobordism of Classifying Spaces
We define algebraic cobordism of classifying spaces, Ω∗(BG) and G-equivariant algebraic cobordism Ω∗G(−) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F (Ω(−)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate Ω(BG) for algebraic groups...
متن کاملEquivariant Algebraic Cobordism
We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.
متن کاملh-cobordism and s-cobordism Theorems: Transfer over Semialgebraic and Nash Categories, Uniform bound and Effectiveness
The h-cobordism theorem is a noted theorem in differential and PL topology. A generalization of the h-cobordism theorem for possibly non simply connected manifolds is the so called s-cobordism theorem. In this paper, we prove semialgebraic and Nash versions of these theorems. That is, starting with semialgebraic or Nash cobordism data, we get a semialgebraic homeomorphism (respectively a Nash d...
متن کاملTorsion Algebraic Cycles and Étale Cobordism
We prove that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of `-adic étale cobordism over an algebraically closed field of positive characteristic. This shows that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of Atiyah, Hirzebruch and Totaro also work in positive
متن کاملFundamental Classes in Algebraic Cobordism
We recall our construction of fundamental classes in the algebraic cobordism of smooth quasi-projective varieties, and show by examples that it is not possible to extend this to fundamental classes, functorial for local complete intersection morphisms, for Cohen-Macaulay varieties.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002