Homology of Linear Groups via Cycles in Bg×x
نویسندگان
چکیده
Homology theories for algebraic varieties are often constructed using simplicial sets of algebraic cycles. For example, Bloch’s higher Chow groups and motivic cohomology, as defined by Suslin and Voevodsky [17], are given in this fashion. In this paper, we construct homology groups Hi(X,G), where G is an algebraic group and X is a variety, by considering cycles on the simplicial scheme BG×X, an idea first suggested by Andrei Suslin. If X = Spec(R) is an affine scheme, then there is a natural map
منابع مشابه
Topological K-(co-)homology of Classifying Spaces of Discrete Groups
Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction EG×G X of a proper G-CW -complex X satisfying certain finiteness conditions. In particular we give formulas computing the topological K-(co)homology K∗(BG) and K(BG) up to finite abelian torsion groups. They apply for instance to arithmetic groups, word hyperbolic gr...
متن کاملMechanical properties of electrophoretically deposited 45S5 bioglass-graphene oxide composite coatings
Bioglass-graphene oxide composites can be served as a high-potential candidate for biomedical applications due to its specific mechanical properties. In this study, the 45S5 bioactive glass (BG) - graphene oxide (GO) composite containing 2 wt. % GO was coated on titanium alloy via electrophoretic deposition process (EPD). The synthesized GO was incorporated into BG coating to improve the mechan...
متن کاملBousfield Localizations of Classifying Spaces of Nilpotent Groups
Let G be a finitely generated nilpotent group. The object of this paper is to identify the Bousfield localization LhBG of the classifying space BG with respect to a multiplicative complex oriented homology theory h∗. We show that LhBG is the same as the localization of BG with respect to the ordinary homology theory determined by the ring h0. This is similar to what happens when one localizes a...
متن کاملOn The homotopy theory of p-completed classifying spaces
Let G be a discrete group and let BG denote its classifying space. Recall that a group is said to be perfect if it is equal to it’s own commutator subgroup. If G is an arbitrary group, then write BG for the Quillen “plus” construction applied to BG with respect to the unique maximal normal perfect subgroup ΠG of G [32]. The space BG can be obtained by attaching 2 and 3 cells to BG and has the d...
متن کاملHomology Approximations for Classifying Spaces of Finite Groups
where D is some small category, F is a functor from D to the category of spaces, and, for each object d of D, F (d) has the homotopy type of BH for some subgroup H of G. An expression like 1.1 is sometimes called a homology approximation to BG or a homology decomposition of BG, and can be used either to make calculations with BG or to prove general theorems about BG by induction. (Of course an ...
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 2003