عنوان

On the Tangent :

(Number (ISBN

0691120439

(Number (ISBN

1400837170

(Number (ISBN

9780691120430

(Number (ISBN

9781400837175

Erroneous ISBN

0691120447

Erroneous ISBN

9780691120447

Title Proper

On the Tangent :

General Material Designation

[Book]

Other Title Information

space to the space of algebraic cycles on a smooth algebraic variety /

First Statement of Responsibility

Mark Green and Phillip Griffiths.

Place of Publication, Distribution, etc.

Princeton :

Name of Publisher, Distributor, etc.

Princeton University Press,

Date of Publication, Distribution, etc.

2004.

Specific Material Designation and Extent of Item

1 online resource (vi, 200 pages) :

Other Physical Details

illustrations.

Series Title

Annals of mathematics studies ;

Volume Designation

no. 157

Text of Note

Includes bibliographical references (pages 195-197) and index.

Text of Note

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 Angéniol 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.

Source for Acquisition/Subscription Address

JSTOR

Stock Number

22573/ctt249rdh

Title

On the Tangent.

Algebraic cycles.

Geometry, Algebraic.

Hodge theory.

Cycles algébriques.

Géométrie algébrique.

Hodge, Théorie de.

Algebraic cycles.

Geometry, Algebraic.

Hodge theory.

MATHEMATICS-- Algebra-- Abstract.

MATHEMATICS-- Geometry-- Algebraic.

MAT-- 012010

MAT002010

Number

Edition

Class number

Book number

Green, M., (Mark)

Date of Transaction

20200824082318.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y