Jacobi-bernoulli Cohomology and Deformations of Schemes and Maps
ثبت نشده
چکیده
We introduce a notion of Jacobi-Bernoulli cohomology associated to a semisimplicial Lie algebra (SELA). For an algebraic scheme X over C, we construct a tangent SELA TX and show that the Jacobi-Bernoulli cohomology of TX is related to infinitesimal deformations of X.
منابع مشابه
S ep 2 00 6 BERNOULLI NUMBERS AND DEFORMATIONS OF SCHEMES AND MAPS
We introduce a notion of Jacobi-Bernoulli cohomology associated to a semi-simplicial Lie algebra (SELA). For an algebraic scheme X over C, we construct a tangent SELA TX and show that the Jacobi-Bernoulli cohomology of TX is related to infinitesimal deformations of X. 0. Overview The 'usual' deformation theory, e.g. of complex structures, in the manner of Kodaira-Spencer-Grothendieck (cf. e.g. ...
متن کاملOn continuous cohomology of locally compact Abelian groups and bilinear maps
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
متن کاملAbel-jacobi Mappings and Finiteness of Motivic Cohomology Groups
1. Notation and generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 2. Varieties over local fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3. Varieties over p-adic fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4. Number field ca...
متن کاملList of contributions
Harmonic maps between Riemannian manifolds are maps which extremize a certain natural energy functional; they appear in particle physics as nonlinear sigma models. Their infinitesimal deformations are called Jacobi fields. It is important to know whether the Jacobi fields along the harmonic maps between given Riemannian manifolds are integrable, i.e., arise from genuine variations through harmo...
متن کاملArithmetic Hodge Structure and Higher Abel-jacobi Maps
In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford in...
متن کامل