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## Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

*Claire Voisin*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691160504
- eISBN:
- 9781400850532
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160504.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. ... More

## Lectures on Algebraic Cycles and Chow Groups

*Jacob Murre*

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)*

### in Hodge Theory (MN-49)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.003.0009
- Subject:
- Mathematics, Geometry / Topology

This chapter showcases five lectures on algebraic cycles and Chow groups. The first two lectures are over an arbitrary field, where they examine algebraic cycles, Chow groups, and equivalence ... More

## Introduction

*Claire Voisin*

### in Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691160504
- eISBN:
- 9781400850532
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160504.003.0001
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses some crucial notions to the interplay between cohomology and Chow groups, and also to the consequences, for the topology of a family of smooth projective varieties, of ... More

## Hodge Theory (MN-49)

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dung Tráng*

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The ... More

## The Norm Residue Theorem in Motivic Cohomology

*Christian Haesemeyer and Charles A. Weibel*

- Published in print:
- 2019
- Published Online:
- January 2020
- ISBN:
- 9780691191041
- eISBN:
- 9780691189635
- Item type:
- book

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191041.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these ... More

## Review of Hodge theory and algebraic cycles

*Claire Voisin*

### in Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691160504
- eISBN:
- 9781400850532
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691160504.003.0002
- Subject:
- Mathematics, Geometry / Topology

This chapter provides the background for the studies to be undertaken in succeeding chapters. It reviews Chow groups, correspondences and motives on the purely algebraic side, cycle classes, and ... More

## The Spread Philosophy in the Study of Algebraic Cycles

*Mark L. Green*

*Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng (eds)*

### in Hodge Theory (MN-49)

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691161341
- eISBN:
- 9781400851478
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691161341.003.0010
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the spread philosophy in the study of algebraic cycles, in order to make use of a geometry by considering a variation of Hodge structure where D is the Hodge domain (or the ... More

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