Laumon G. — Cohomology of Drinfeld modular varieties (Part 1) :: Электронная библиотека попечительского совета мехмата МГУ

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Laumon G. — Cohomology of Drinfeld modular varieties (Part 1)

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Название: Cohomology of Drinfeld modular varieties (Part 1)

Автор: Laumon G.

Аннотация:

Cohomology of Drinfeld Modular Varieties aims to provide an introduction to both the subject of the title and the Langlands correspondence for function fields. These varieties are the analogs for function fields of Shimura varieties over number fields. This present volume is devoted to the geometry of these varieties and to the local harmonic analysis needed to compute their cohomology. To keep the presentation as accessible as possible, the author considers the simpler case of function rather than number fields; nevertheless, many important features can still be illustrated. It will be welcomed by workers in number theory and representation theory.

Язык:

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 344

Добавлена в каталог: 11.03.2005

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Предметный указатель

$(F,\infty,o)$ -type of rank d      26
$(\sigma–K_{P,r})$ -invariant constant term (along a parabolic subgroup)      97
$K_{P}$ -invariant constant term (along a parabolic subgroup)      91
$\sigma$ -centralizer      93
$\sigma$ -closed element      96
$\sigma$ -conjugate      93
$\sigma$ -elliptic      102
$\sigma$ -orbit      96
$\varpi_{o}$ -divisible scheme in $\mathcal{O}_{o}$ -modules      33
Admissible representation      160 290
Admit a central character      289
Affine Weyl group      181
Base change homomorphism      83
Brauer group      249
Bruhat — Tits building      133
Bruhat — Tits decomposition      183
Cartan decomposition      76
Central algebra (over a field)      249
Central character      289
Central division algebra (over a field)      249
Chamber (of the Bruhat — Tits building)      133
CHARACTER      291
Characteristic (of a Drinfeld module )      5
Closed element      87
Cohomology      216 322
Commutant      250
Compactly induced representation      326
Constant term (along a parabolic subgroup)      78
Contragredient representation      288
Cuspidal (quasi-cuspidal) representation      165 312
Cyclic representation      234
Cyclic vector      234
Degree (of an isogeny)      21
Dieudonne $\mathcal{F}_{o}$ -module      31
Dieudonne $\mathcal{O}_{o}$ -module      31
Dieudonne module of a Drinfeld module      35
Drinfeld A-module      4
Elliptic      60
Elliptic at the place $\infty$       60
Equivalent (central simple algebras)      249
Euler — Poincare characteristic      217
Euler — Poincare function      132
Euler — Poincare measure      138
Facet (of the Bruhat — Tits building)      133
Frobenius isogeny      23
Good position (with respect to a parabolic subgroup)      91
Good position (with respect to a triple)      163 297
Haar measure      69
Hecke algebra      13 75 129
Hecke eigenvalue (of a spherical representation)      188
Hecke function      101
Hecke operator      15
Height (of an isogeny)      20 21
Hermitian contragredient      327
Hermitian representation      327
I-division point      5
Induction functor      160 293

Inner twist      68
Inner twisting      68
Invariant at of a central simple algebra (over a function field)      254
Invariant of a central simple algebra (over a local field)      254
Isogeny      20
Isogeny (between Drinfeld modules)      20
Iwahori subgroup      129
Iwasawa decomposition      77
Kottwitz function      133
Lefschetz number (of a correspondance)      52
Length function (on the affine Weyl group)      181
Level-I structure      6
Matrix coefficient      311
Modular variety      7
Multiplicity (of a slope)      32
Non-degenerate module      286
Norm      93
Orbital integral      57 91
Parahoric subgroup (corresponding to a parabolic subgroup)      131
Principal congruence subgroup of level N      162
Principal series representation      168
q-binomial coefficient      281
r-admissible ( $\sigma$ -closed element)      101
r-admissible (at the place o)      55 60
r-admissible (closed element)      98
Rank (of a Drinfeld module)      4
Rational Haar measure      285
Representation      284
Restriction functor (or modified Jacquet functor)      160 293
Satake isomorphism      77
Satake transform      77 78
Simple algebra      250
Slope (of a Dieudonne module)      32
Smooth representation      160 284
Smooth vector      284
Spectral decomposition      238
Spectral measure      237
Spherical representation      187
Square-integrable representation      220 329
Stabilizer (of a vector in a representation)      284
Steinberg representation      193
Tamagawa measure      70
Tamagawa number      70
Tate module (of a Drinfeld module)      28
Tensor product      334
Transfer (of a conjugacy class)      60
Transfer (of local or global Haar measures)      69
Twisted orbital integral      57 96
Unitarizable representation      220 327
Unitary continuous representation      234
Unramified principal series representation      178
Vertex (of the Bruhat — Tits building)      133
Very cuspidal function      133
Wall (of the Bruhat — Tits building)      133
Weil $(F,\infty,o)$ -pair of rank d      23
x-adic cohomology group      31
Yoneda extension (vector space or bifunctor)      216 324

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