**University Lecture Series**

Volume: 61;
2013;
149 pp;
Softcover

MSC: Primary 14; 19;

Print ISBN: 978-0-8218-9434-7

Product Code: ULECT/61

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

**Electronic ISBN: 978-1-4704-1039-1
Product Code: ULECT/61.E**

List Price: $44.00

AMS Member Price: $35.20

MAA Member Price: $39.60

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#### Supplemental Materials

# Lectures on the Theory of Pure Motives

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*Jacob P. Murre; Jan Nagel; Chris A. M. Peters*

The theory of motives was created by Grothendieck in the 1960s as he
searched for a universal cohomology theory for algebraic
varieties. The theory of pure motives is well established as far as
the construction is concerned. Pure motives are expected to have a
number of additional properties predicted by Grothendieck's standard
conjectures, but these conjectures remain wide open. The theory for
mixed motives is still incomplete.

This book deals primarily with the theory of pure motives. The
exposition begins with the fundamentals: Grothendieck's construction
of the category of pure motives and examples. Next, the standard
conjectures and the famous theorem of Jannsen on the category of the
numerical motives are discussed. Following this, the important theory
of finite dimensionality is covered. The concept of Chow-Künneth
decomposition is introduced, with discussion of the known results and
the related conjectures, in particular the conjectures of
Bloch-Beilinson type. We finish with a chapter on relative motives and
a chapter giving a short introduction to Voevodsky's theory of mixed
motives.

#### Readership

Graduate students and research mathematicians interested in algebraic cycles and motives.

#### Table of Contents

# Table of Contents

## Lectures on the Theory of Pure Motives

- Cover Cover11 free
- Title page i2 free
- Contents iii4 free
- Introduction v6 free
- Algebraic cycles and equivalence relations 112 free
- Survey of some of the main results on Chow groups 1324
- Proof of the theorem of Voisin-Voevodsky 1930
- Motives: Construction and first properties 2334
- On Grothendieck’s standard conjectures 3546
- Finite dimensionality of motives 4354
- Properties of finite dimensional motives 5162
- Chow-Künneth decomposition; The Picard and Albanese motive 6778
- Chow-Künneth decomposition in a special case 8394
- On the conjectural Bloch-Beilinson filtration 8596
- Relative Chow-Künneth decomposition 105116
- Surfaces fibered over a curve 119130
- Beyond pure motives 123134
- The category of motivic complexes 135146
- Bibliography 139150
- Index of notation 145156 free
- Index 147158 free
- Back Cover Back Cover1162