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Wildeshaus J. — Realizations Of Polylogarithms
Wildeshaus J. — Realizations Of Polylogarithms

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Название: Realizations Of Polylogarithms

Автор: Wildeshaus J.

Аннотация:

The principal aim of the book is to document the sheaf theoretical foundations of the field of polylogarithms, generalizing the approach of Heilinson, Deligne, and Levin to the context of Shimura varieties. Readers interested in this construction will find it necessary to read the whole of the first and the third part. From the second part, one needs the fact that the so-called logarithmic sheaf lies in the image of the canonical construction functor (2.1, 4.4, and 6.5 respectively). The results on compatibility of Hochschild cohomology and higher direct images (2.3, 3.5, 4.7, and 6.6 respectively) are then dire< t consequences ol the results of the first par'.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 343

Добавлена в каталог: 22.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$Gau\beta$ — Manin connection      105
(S, L)-constructible      67
(S, L)-perverse sheaf      67
Admissible variation      58
Admissible variation, unipotent      41
Artin motive      117
Bifiltered vector bundle      48
Bifiltered vector bundle, canonical construction      104
Bifiltered vector bundle, generic      52
Canonical construction of bifiltered bundles      104
Canonical construction of l-adic sheaves      112
Canonical construction of mixed systems      127
Canonical construction of variations      94
Canonical model      87
Classical logarithm, Hodge version of      214
Classical logarithm, l-adic version of      232
Classical logarithm, local system underlying      212
Classical polylogarithm, Hodge version of      220
Classical polylogarithm, l-adic version of      233
Classical polylogarithm, local system underlying      212
CM-motive      117
Cohomology, continuous      40
Cohomology, Deligne      321
Cohomology, Galois      236
Cohomology, Hochschild      33
Continuous cohomology      40
Debye polylogarithin, classical      217
Debye polylogarithin, elliptic      278
Deligne torus      83
Descent of coherent subsheaf      51
Distribution property of classical polylogarithm      225
Distribution property of elliptic polylogarithm      299
Eichler — Shimura homomorphism      305
Eisenstein series      282
Elliptic logarithm, Hodge version of      275
Elliptic logarithm, local system underlying      263
Elliptic polylogarithm, Hodge version of      293
Elliptic polylogarithm, local system underlying      267
Extension of Galois modules      236
Extension of Hodge structures      324
Extension of Hodge — de Rham structures      324
Extension of variations      222
Fibre functor      29
Geometric origin      52
Griffiths transversality      49
Hecke character      335
Higher logarithm, classical      217
Higher logarithm, elliptic      289
Hochschild cohomology      33
Hodge module      66
Hodge structure      41
Hodge structure of CM-type      117
Hodge structure, extension of      324
Kronecker double series      330
l-adic representation      39
Levi decomposition      87
Levi section      87
Levi section of Shimura data      87
Levi section, classical case      206
Levi section, elliptic case      260
Levi section, norm compatibility      192
Levi section, value at      191
Lisse l-adic sheaf      44
Lisse l-adic sheaf, generic pro-unipotent      46
Lisse l-adic sheaf, mixed      44
Lisse l-adic sheaf, mixed, $\pi$-unipotent      55
Lisse l-adic sheaf, mixed, unipotent      44
Lisse l-adic sheaf, mixed, with a weight filtration      44
Local system underlying, classical logarithm      212
Local system underlying, classical polylogarithm      212
Local system underlying, elliptic logarithm      263
Local system underlying, elliptic polylogarithm      267
Logarithmic bifiltered pro-bundle      106
Logarithmic l-adic pro-sheaf      113
Logarithmic l-adic pro-sheaf, classical      232
Logarithmic mixed system      132
Logarithmic pro-variation      94
Logarithmic pro-variation, classical      214
Logarithmic pro-variation, elliptic      275
Logarithmic sheaf      150
Logarithmic sheaf, splitting principle for      190
Malcev — Lie algebra      38
Manin — Drinfeld principle      319
Mixed Hodge module      66
Mixed system of perverse sheaves      68
Mixed system of smooth sheaves      48
Mixed system of smooth sheaves, $\pi$-unipotent      61
Mixed system of smooth sheaves, canonical construction      127
Mixed system of smooth sheaves, generic pro-unipotent      53
Mixed system of smooth sheaves, Tate twist      50
Mixed system of smooth sheaves, unipotent      50
Monodromy representation      41
Motive, Artin      117
Motive, CM-      117
NC-divisor      45
NC-divisor, relative to S      46
NC-divisor, relative to S in the strong sense      46
Neat      85
Norm character      203
Norm compatibility      187
Norm compatibility of classical polylogarithm      225
Norm compatibility of elliptic polylogarithm      299
Norm compatibility of values at Levi sections      192
Of type (R)      55
Of type (R) over $O_S$      48
Path space variation      59
Perverse cohomology functors      67
Perverse sheaf      66
Perverse sheaf, mixed      66
Perverse sheaf, mixed system of      68
Perverse sheaf, wrt, (S, L)      67
Polarization      50
Polylogarithmic extension      161
Polylogarithmic extension, classical, Hodge version of      220
Polylogarithmic extension, classical, l-adic version of      233
Polylogarithmic extension, elliptic, Hodge version of      293
Polylogarithmic extension, large      161
Polylogarithmic extension, norm compatibility of      187
Polylogarithmic extension, rigidity of      163
Polylogarithmic extension, small      182
Polylogarithmic extension, value at Levi section of      191
Pontryagin pairing      330
Pro-unipotent envelope      38
Properly discontinuous      86
Pseudo-nilpotent      40
purity      154
Rational $K(\pi      1)$ 65
Reflex field      87
Regular at infinity      48
Regular holonomic $\mathcal D$-module      109
Relative duality      154
Relative NC-divisor      46
Representation, l-adic      39
Representation, mixed      112
Representation, monodromy      41
Representation, pure      112
Representation, twisted      118
Riemann — Hilbert correspondence      110
Rigidity      163
Rigidity for values at Levi sections of the elliptic polylogarithm      304
Serre group      117
Sheaf      68
Sheaf, topological      68
Shimura data of abelian type      113
Shimura data, embedding of      86
Shimura data, irreducible      89
Shimura data, mixed      83
Shimura data, morphism of      86
Shimura data, pure      84
Shimura data, reflex field      87
Shimura data, twist of      120
Shimura data, unipotent extension of      203
Shimura variety      85
Shimura variety, canonical model      87
Shimura variety, very regular model of a diagram of      158
Shimura variety, very regular model of a morphism of      115
Shimura’s condition      334
Shioda’s theorem      102
Siegel function      316
Special point      119
Spectral sequence, Hochschild — Serre      167
Spectral sequence, Leray      159
Splitting principle      190
Standard principal bundle      105
Tamagawa number conjecture      242
Taniyama group      117
Tannakian category      28
Tannakian dual      29
Tate twist      50
Tensor category      28
Twist by an automorphism of $\mathbb C$      118
Twist of a representation      118
Twist of Shimura data      120
Twist, Tate      50
Unipotent envelope      38
Unipotent extension of Shimura data      203
Unipotent generic l-adic sheaf      46
Unipotent generic mixed system      53
Unipotent generic variation      43
Unipotent lisse l-adic sheaf      44
Unipotent variation      41
Unipotent, $K(\pi      1)$ 64
Unipotent, relatively, lisse l-adic sheaf      55
Unipotent, relatively, mixed system      61
Unipotent, relatively, variation      58
Universal enveloping algebra      30
Universal property of generic sheaf      60
Value at Levi section      191
Value at Levi section of classical poly logarithm, Hodge version of      227
Value at Levi section of classical poly logarithm, l-adic version of      237
Value at Levi section of classical poly logarithm, mixed systems version of      243
Value at Levi section of elliptic polylogarithm for a single curve      332
Value at Levi section of elliptic polylogarithm, Hodge version of      307
Variation of Hodge structure, admissible      58
Variation of Hodge structure, admissible, $\pi$-unipotent      58
Variation of Hodge structure, admissible, unipotent      41
Variation of Hodge structure, canonical      43
Variation of Hodge structure, canonical construction      94
Variation of Hodge structure, extension of      222
Variation of Hodge structure, generic pro-unipotent      43
Variation of Hodge structure, Nilpotent Orbit Theorem      52
Variation of Hodge structure, over $\mathbb R$      63
Variation of Hodge structure, path space      59
Variation of Hodge structure, Theorem of Hain — Zucker      42
Variation of Hodge-de Rham structure      311
Variation of Hodge-de Rham structure, extension of      312
Vector bundle, bifiltered      48
Vector bundle, bifiltered, canonical construction      104
Vector bundle, bifiltered, generic      52
Very regular model      150
Very regular model of a diagram      158
Very regular model of a morphism      115
Very regular model of a morphism with a section      150
Weak fibration      58
Zagier’s conjecture      333
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