MIXED MOTIVES

By ABIGAIL CLARK

CONTENTS PART I MOTIVES INTRODUCTION: PART I CHAPTER I THE MOTIVIC CATEGORY 1 THE MOTIVIC DG CATEGORY 2 THE TRIANGULATED MOTIVIC CATEGORY 3 STRUCTURE OF THE MOTIVIC CATEGORIES CHAPTER II MOTIVIC COHOMOLOGY AND HIGHER CHOW GROUPS 1 HYPERCOHOMOLOGY IN THE MOTIVIC CATEGORY 2 HIGHER CHOW GROUPS 3 THE MOTIVIC CYCLE MAP CHAPTER III K-THEORY AND MOTIVES 1 CHERN CLASSES 2 PUSH-FORWARD 3 RIEMANN-ROCH CHAPTER IV HOMOLOGY, COHOMOLOGY, AND DUALITY 1 DUALITY 2 CLASSICAL CONSTRUCTIONS 3 MOTIVES OVER A PERFECT ?ELD CHAPTER V REALIZATION OF THE MOTIVIC CATEGORY 1 REALIZATION FOR GEOMETRIC COHOMOLOGY 2 CONCRETE REALIZATIONS CHAPTER VI MOTIVIC CONSTRUCTIONS AND COMPARISONS 1 MOTIVIC CONSTRUCTIONS 2 COMPARISON WITH THE CATEGORY DMGM(K) PART II CATEGORICAL ALGEBRA INTRODUCTION: PART II CHAPTER I SYMMETRIC MONOIDAL STRUCTURES 1 FOUNDATIONAL MATERIAL 2 CONSTRUCTIONS AND COMPUTATIONS CHAPTER II DG CATEGORIES AND TRIANGULATED CATEGORIES 1 DI?ERENTIAL GRADED CATEGORIES 2 COMPLEXES AND TRIANGULATED CATEGORIES 3 CONSTRUCTIONS CHAPTER III SIMPLICIAL AND COSIMPLICIAL CONSTRUCTIONS 1 COMPLEXES ARISING FROM SIMPLICIAL AND COSIMPLICIAL OBJECTS 2 CATEGORICAL COCHAIN OPERATIONS 3 HOMOTOPY LIMITS CHAPTER IV CANONICAL MODELS FOR COHOMOLOGY 1 SHEAVES, SITES, AND TOPOI 2 CANONICAL RESOLUTIONS