ARITHMETIC DUALITY THEOREMS

By V. LAONO

CONTENTS I GALOIS COHOMOLOGY PRELIMINARIES DUALITY RELATIVE TO A CLASS FORMATION LOCAL ?ELDS ABELIAN VARIETIES OVER LOCAL ?ELDS GLOBAL ?ELDS GLOBAL EULER-POINCAR´E CHARACTERISTICS ABELIAN VARIETIES OVER GLOBAL ?ELDS AN APPLICATION TO THE CONJECTURE OF BIRCH AND SWINNERTON-DYER ABELIAN CLASS ?ELD THEORY OTHER APPLICATIONS APPENDIX A: CLASS ?ELD THEORY FOR FUNCTION ?ELDS II ETALE COHOMOLOGY LOCAL RESULTS GLOBAL RESULTS: PRELIMINARY CALCULATIONS GLOBAL RESULTS: THE MAIN THEOREM GLOBAL RESULTS: COMPLEMENTS GLOBAL RESULTS: ABELIAN SCHEMES GLOBAL RESULTS: SINGULAR SCHEMES GLOBAL RESULTS: HIGHER DIMENSIONS III FLAT COHOMOLOGY LOCAL RESULTS: MIXED CHARACTERISTIC, ?NITE GROUP SCHEMES LOCAL RESULTS: MIXED CHARACTERISTIC, ABELIAN VARIETIES GLOBAL RESULTS: NUMBER ?ELD CASE LOCAL RESULTS: MIXED CHARACTERISTIC, PERFECT RESIDUE ?ELD TWO EXACT SEQUENCES LOCAL ?ELDS OF CHARACTERISTIC P LOCAL RESULTS: EQUICHARACTERISTIC, ?NITE RESIDUE ?ELD GLOBAL RESULTS: CURVES OVER ?NITE ?ELDS, ?NITE SHEAVES GLOBAL RESULTS: CURVES OVER ?NITE ?ELDS, N´ERON MODELS LOCAL RESULTS: EQUICHARACTERISTIC, PERFECT RESIDUE ?ELD GLOBAL RESULTS: CURVES OVER PERFECT ?ELDS APPENDIX A: EMBEDDING ?NITE GROUP SCHEMES APPENDIX B: EXTENDING ?NITE GROUP SCHEMES APPENDIX C: BIEXTENSIONS AND N´ERON MODELS