In recent years, considerable progress has been made in studying
algebraic cycles using infinitesimal methods. These methods have
usually been applied to Hodge-theoretic constructions such as the
cycle class and the Abel-Jacobi map. Substantial advances have also
occurred in the infinitesimal theory for subvarieties of a given
smooth variety, centered around the normal bundle and the
obstructions coming from the normal bundle's first cohomology
group. Here, Mark Green and Phillip Griffiths set forth the initial
stages of an infinitesimal theory for algebraic cycles.
The book aims in part to understand the geometric basis and the
limitations of Spencer Bloch's beautiful formula for the tangent
space to Chow groups. Bloch's formula is motivated by algebraic
K-theory and involves differentials over Q. The theory developed
here is characterized by the appearance of arithmetic
considerations even in the local infinitesimal theory of algebraic
cycles. The map from the tangent space to the Hilbert scheme to the
tangent space to algebraic cycles passes through a variant of an
interesting construction in commutative algebra due to Angeniol and
Lejeune-Jalabert. The link between the theory given here and
Bloch's formula arises from an interpretation of the Cousin flasque
resolution of differentials over Q as the tangent sequence to the
Gersten resolution in algebraic K-theory. The case of 0-cycles on a
surface is used for illustrative purposes to avoid undue technical
complications."
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!