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Levine M. — Mixed motives
Levine M. — Mixed motives



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Название: Mixed motives

Автор: Levine M.

Аннотация:

The author constructs and describes a triangulated category of mixed motives over an arbitrary base scheme. The resulting cohomology theory satisfies the Bloch-Ogus axioms; if the base scheme is a smooth scheme of dimension at most one over a field, this cohomology theory agrees with Bloch's higher Chow groups. Most of the classical constructions of cohomology can be made in the motivic setting, including Chern classes from higher X-theory, push-forward for proper maps, Riemann-Roch, duality, as well as an associated motivic homology, Borel-Moore homology and cohomology with compact supports. The motivic category admits a realization functor for each Bloch-Ogus cohomology theory which satisfies certain axioms; as examples the author constructs Betti, etale, and Hodge realizations over smooth base schemes.
This book is a combination of foundational constructions in the theory of motives, together with results relating motivic cohomology with more explicit constructions, such as Bloch's higher Chow groups. It is aimed at research mathematicians interested in algebraic cycles, motives and X-theory, starting at the graduate level. It presupposes a basic background in algebraic geometry
and commutative algebra.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1998

Количество страниц: 515

Добавлена в каталог: 23.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Mixed Hodge modules      282
Monoidal category      375
Motive of a cosimplicial scheme      27—28
Motive of a cubical hyperresolution      241
Motive of a cubical hyperresolution, blow-up diagram for      241
Motive of a diagram      34—35
Motive of a diagram, distinguished triangle      35—36
Motive of a diagram, products      36
Motive of a diagram, properties      156
Motive of a k-scheme      241
Motive of a k-scheme, Borel — Moore      251—253
Motive of a k-scheme, cohomological      246—249
Motive of a k-scheme, compactly supported      251—253
Motive of a k-scheme, comparisons      250
Motive of a k-scheme, homological      249—250
Motive of a k-scheme, products      248
Motive of a non-degenerate simplicial scheme      30
Motive of a simplicial scheme      28—31
Motive of a variety      21
Motive of an n-cube      31—32
Motive with support      21
Motive with support of a diagram      156
Motive with support of a simplicial scheme      109
Motive, Borel — Moore      153
Motive, Borel — Moore for singular schemes      225 227—231
Motive, Borel — Moore with support      153 226
Motive, Borel — Moore, cap products      217
Motive, Borel — Moore, functoriality      153
Motive, Borel — Moore, properties      217
Motive, Cech resolution      54 58
Motive, compactly supported      215
Motive, compactly supported for singular schemes      227—231
Motive, compactly supported, cup products      217
Motive, compactly supported, properties      217
Motive, fundamental properties      19
Motive, homological      215
Motive, homological, cap products      217
Motive, homological, projection formula      217
Motive, homological, properties      216—217
Motive, homological, relative      216
Motive, homological, Thorn isomorphism      216
Motive, Lefschetz      23
Motive, open cover      54 58
Motive, open cover, push-forward      56
Motive, relative      31 33—34 123
Motive, relative with support      34 124
Motive, relative, duality for      219—224
Motivic, Borel — Moore functor      216
Motivic, Borel — Moore homology      215
Motivic, cohomology      21 22
Motivic, cohomology and higher Chow groups      103
Motivic, cohomology and homology of GL      121—122
Motivic, cohomology as Zariski hypercohomology      89
Motivic, cohomology for simplicial schemes      30—31
Motivic, cohomology of a diagram      36
Motivic, cohomology with compact support      215
Motivic, cohomology, mod n      21
Motivic, cohomology, relative      34 123 218 225
Motivic, cohomology, semi-purity      140
Motivic, cohomology, special properties      89
Motivic, cycle complex      67
Motivic, cycles functor      38
Motivic, DG category      12 36
Motivic, DG category, construction      12—16
Motivic, DG category, structure      36—38
Motivic, functor with compact support      216
Motivic, Gersten complex      91
Motivic, Gersten conjecture      92
Motivic, Gersten resolution      93
Motivic, homological functor      215
Motivic, homology      215
Motivic, homology, relative      225
Motivic, homotopy category      40
Motivic, homotopy category, structure      40—44
Motivic, hypercohomology      62
Motivic, local to global spectral sequence      90
Motivic, polylogarithm      303
Motivic, polylogarithm as a diagram of schemes      303—304
Motivic, polylogarithm as a motive      309
Motivic, polylogarithm, distinguished triangle      309
Motivic, polylogarithm, spectral sequence      305—306
Motivic, pull-back      24
Motivic, Quillen spectral sequence      91
Motivic, suspension      68 70 76 187
Motivic, triangulated category      16 44
Motivic, triangulated category, definition      17—19
Motivic, triangulated category, structure      44—47
Motivic, triangulated Tate category      234 235
Moving Lemma      20 94 96 102
Moving lemma for diagrams      36
Moving lemma, isomorphism      18
Multiplication for a cosimplicial functor      464
Multiplication in a symmetric monoidal category      453
Multiplication of cosimplicial objects      452
Multiplication, commutative      453
Multiplicative system      424—425
N-cubes      32
N-cubes, distinguished triangle      33
N-cubes, lifting      32
N-cubes, relative motives      31
Negligible complexes      270
Nerve of a category      468
Nisnevic sheaf with transfers      311
Nisnevic sheaf with transfers, homotopy invariant      311
Nisnevic topology      311
Normal crossing subschemes      208
Normalized complex of a cosimplicial abelian group      275
Normalized complex of an inverse system      269
Octahedra      429
Operad      444
Pentagonal identity      375
Permutative bi-module      402—403
Perverse sheaf      282
Plus construction and Q-construction      359
Plus construction for diagrams      361—362
Plus construction for diagrams, H-group structure      365
Plus construction for rings      359
Plus construction for schemes      360
Point      483
Point, associated pro-object      485
Point, conservative family      484
Point, neighborhood of a      485
Point, stalk      484
Pre-additive category      378
Pre-differential graded category      379
Pre-graded category      378
Pre-tensor category      382
Pre-Tr      410—411
Presheaf of sets      482
Presheaf with values in a category      482
Products and holim      476—479
Products for cosimplicial objects      452
Products for equi-dimensional cycles      355
Products for motives of diagrams      36
Products for motives of simplicial schemes      31
Products for motivic Borel — Moore homology      217
Products for motivic cohomology      22
Products for motivic cohomology with compact support      217
Products for motivic homology      217
Products, Alexander — Whitney      452
Projection formula for a projection      144
Projection formula for a projective morphism      150
Projection formula for an embedding      136
Projective bundle formula      113 114
Properties      66
Pseudo-abelian hull      427
Pseudo-abelian hull of a tensor category      427
Pseudo-abelian hull of a triangulated category      427—433
Pseudo-tensor functor      382—383
Push-forward for a projection      142
Push-forward for a projective morphism      146
Push-forward for a projective morphism, compatibility with cycle classes      152
Push-forward for a projective morphism, compatibility with products      151
Push-forward for a projective morphism, compatibility with pull-back      150
Push-forward for a projective morphism, definition      146—147
Push-forward for a projective morphism, functoriality      149
Push-forward for a projective morphism, naturality      151
Push-forward for diagrams      153 159—161
Push-forward for K-theory      171—172
Push-forward, additional properties      151
Q-construction      358
Real Frobenius      268
Realization for geometric cohomology theories      261
Realization, Betti      267
Realization, Betti, complex      267—268
Realization, Betti, real      268
Realization, Chow      79 80
Realization, etale      268 271—272
Realization, etale, $\mathbb{Q}_l$      272
Realization, etale, mod n      272
Realization, functor      260 266
Realization, functor for cohomology      267
Realization, Hodge      273 280 281
Realization, Hodge over a smooth base      282 284
Realization, Hodge, real      281 282
Realization, motivic      284 291
Reduction      240
Relative cycles      331
Relativization, distinguished triangle      33
Relativization, sequence      126 129
Relativization, sequence, compatibility with Chern classes      128—130
Resolution of singularities      237
Riemann — Roch for singular schemes      231 233
Riemann — Roch for smooth schemes      176 177
Riemann — Roch without denominators      171 174
S-smooth stratification      225
Semi-monoidal category      375—376
Semi-monoidal category, strictly associative      375
Sheaf of -R-modules      486
Sheaf of -R-modules, flat      497
Sheaf of sets      482
Sheaf with values in a category      482
Sheafification of a presheaf      482
Simplicial and cosimplicial objects      449
Simplicial closed subset      109—110
Simplicial schemes, lifting      29
Simplicial schemes, line bundles on      112
Simplicial schemes, vector bundles on      110
Smoothly decomposable scheme      225
Splitting idempotents      433
Splitting principle for $K_0$      164
Splitting principle for the motive of a diagram      161
Splitting principle for the motive of a simplicial scheme      116
Stabilization map      358
Stalk      484
Stalk of a presheaf      486
Stalk of a sheaf      486
Steinberg relation      295 296
Structured category      377
Support of a cycle      332
Suspension      67
Symmetric monoidal $\mathcal{V}$-category      380
Symmetric monoidal $\mathcal{V}$-category, free      384
Symmetric monoidal category      375 380
Symmetric monoidal category, constructions      383 385 386
Symmetric monoidal category, examples      376
Symmetric monoidal category, graded      436
Symmetric semi-monoidal category      375
Tate mixed Hodge structure      279
Tate twist      20
Tensor category      381
Tensor category, DG      382
Tensor category, DG without unit      382
Tensor category, graded      381
Tensor category, graded without unit      382
Tensor category, triangulated      416
Thick subcategory      424
Thom — Sullivan cochains      275—277
Thom — Sullivan cochains, tempered      287—289
Todd character      176
Todd class      176
Topos      483
Topos as a site      483
Topos with enough points      484
Topos, fiber functor      483
Topos, point of a      483
Total Chern class      116
Total complex functor      412—413
Translation structure      403
Translation structure for complexes over an additive category      409
Translation structure for Pre-Tr      411
Translation structure, free      406—409
Translation structure, free compatible      408
Translation structure, tensor compatible      404
Translation structures      401
Transverse cartesian square      150
Triangulated category      414
Triangulated category of complexes over a DG category      416
Triangulated category, axioms      414—415
Triangulated category, exact functor      415
Triangulated category, five lemma      415
Triangulated category, localization      424—426
Triangulated category, multiplicative system      424—425
Triangulated category, pseudo-abelianization      427
Triangulated category, thick subcategory      424
Triangulated tensor category      416
Triangulated tensor category, localization      426
Triangulation      477
Twisted duality theory      258
Unit isomorphism      18
Unit motive      20
Universal vector bundle      358
Whitney product formula      117
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