Modular forms and special cycles on Shimura curves:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
2006
|
| Schriftenreihe: | Annals of mathematics studies
number 161 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vii, 373 Seiten |
| ISBN: | 0691125503 0691125511 9780691125503 9780691125510 |
Internformat
MARC
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| 084 | |a MAT 120f |2 stub | ||
| 084 | |a MAT 103f |2 stub | ||
| 084 | |a MAT 144f |2 stub | ||
| 100 | 1 | |a Kudla, Stephen S. |d 1950- |e Verfasser |0 (DE-588)139721665 |4 aut | |
| 245 | 1 | 0 | |a Modular forms and special cycles on Shimura curves |c Stephen S. Kudla ; Michael Rapoport ; Tonghai Yang |
| 264 | 1 | |a Princeton, NJ |b Princeton University Press |c 2006 | |
| 264 | 4 | |c © 2006 | |
| 300 | |a vii, 373 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies |v number 161 | |
| 650 | 4 | |a Géométrie algébrique arithmétique | |
| 650 | 4 | |a Shimura, Variétés de | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
| 650 | 4 | |a Shimura varieties | |
| 650 | 0 | 7 | |a Shimura-Kurve |0 (DE-588)4705871-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Arithmetische Geometrie |0 (DE-588)4131383-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eisenstein-Reihe |0 (DE-588)4131762-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Thetafunktion |0 (DE-588)4185175-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Arithmetische Geometrie |0 (DE-588)4131383-5 |D s |
| 689 | 0 | 1 | |a Shimura-Kurve |0 (DE-588)4705871-7 |D s |
| 689 | 0 | 2 | |a Thetafunktion |0 (DE-588)4185175-4 |D s |
| 689 | 0 | 3 | |a Eisenstein-Reihe |0 (DE-588)4131762-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rapoport, Michael |d 1948- |e Verfasser |0 (DE-588)140462945 |4 aut | |
| 700 | 1 | |a Yang, Tonghai |d 1963- |e Verfasser |0 (DE-588)140463003 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4008-3716-8 |
| 830 | 0 | |a Annals of mathematics studies |v number 161 |w (DE-604)BV000000991 |9 161 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014860065&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014860065 | ||
Datensatz im Suchindex
| _version_ | 1804135449242894336 |
|---|---|
| adam_text | Contents
Acknowledgments
ix
Chapter
1.
Introduction
1
Bibliography
21
Chapter
2.
Arithmetic intersection theory on stacks
27
2.1
The one-dimensional case
27
2.2
Рк(М),СЯІ(М),апаСЯІ(М) ЗО
2.3
Green functions
31
2.4
Pic(./Vť),CHz(.M),andCHz(.M)
34
2.5
The pairing
CÌ^CM)
χ
CR1
(M)
-+
CK
(M)
36
2.6
Arakelov heights
38
2.7
The arithmetic adjunction formula
39
Bibliography
43
Chapter
3.
Cycles on Shimura curves
45
3.1
Shimura curves
46
3.2
Uniformization
47
3.3
The Hodge bundle
49
3.4
Special endomorphisms
51
3.5
Green functions
56
3.6
Special 0-cycles
57
Bibliography
68
Chapter
4.
An arithmetic theta function
71
4.1
The structure of arithmetic Chow groups
71
4.2
The arithmetic theta function
77
4.3
The vertical component: definite theta functions
79
4.4
The analytic component: Maass forms
87
4.5
The Mordell-Weil component
94
4.6
Borcherds generating function
96
4.7
An intertwining property
100
Bibliography
102
Chapter
5.
The central derivative of a genus two
Eisenstein
series
105
5.1
Genus two
Eisenstein
series
105
5.2
Nonsingular Fourier coefficients
111
5.3
The Siegel-Weil formula
5.4
Singular coefficients
5.5
Eisenstein
series of genus one
5.6
Вт
5.7
Wt
5.8
The central derivative
—
the rank one case
5.9
The constant term
Bibliography
Vi
CONTENTS
121
137
139
140
144
154
161
165
Chapter
6.
The generating function for O-cycles
167
6.1
ThecaseT>OwithDiff(T,B) = {p}forp|I)(B)
169
6.2
The case
Τ
> 0
with Diff(T, B)
=
{p} for p D(B)
172
6.3
The case of nonsingular
Τ
with sig(T)
= (1,1)
or
(0,2) 175
6.4
Singular terms,
Τ
of rank
1 177
6.5
The constant term,
Τ
= 0 179
Bibliography
180
Chapter
6
Appendix. The case p-2,p D(B)
181
6A.
1
Statement of the result
181
6A.2 Review of the special cycles Z(j), for q(j)
Є
Zp
{0} 186
6A.3 Configurations
188
6A.4 Calculations
191
6A.5 The first
nondiagonal
case
201
Bibliography
204
Chapter
7.
An inner product formula
205
7.1
Statement of the main result
206
7.2
The case t ti is not a square
208
7.3
A weakly admissible Green function
212
7.4
A finer decomposition of special cycles
221
7.5
Application of adjunction
225
7.6
Contributions for
ρ
D(B)
231
7.7
Contributions for
p j D (B)
238
7.8
Computation of the discriminant terms
245
7.9
Comparison for the case ii, i2
> 0,
and M2
=
m2
252
7.10
The case tu i2
< 0
with tit2
=
m2
259
7.11
The constant terms
262
Bibliography
264
Chapter
8.
On the doubling integral
265
8.1
The global doubling integral
266
8.2
Review of Waldspurger s theory
269
8.3
An explicit doubling formula
279
8.4
Local doubling integrals
285
8.5
Appendix: Coordinates on metaplectic groups
320
Bibliography
346
CONTENTS
VU
Chapter
9.
Central derivatives of L-functions
351
9.1
The arithmetic theta lift
351
9.2
The arithmetic inner product formula
356
9.3
The relation with classical newforms
365
Bibliography
369
Index
371
|
| adam_txt |
Contents
Acknowledgments
ix
Chapter
1.
Introduction
1
Bibliography
21
Chapter
2.
Arithmetic intersection theory on stacks
27
2.1
The one-dimensional case
27
2.2
Рк(М),СЯІ(М),апаСЯІ(М) ЗО
2.3
Green functions
31
2.4
Pic(./Vť),CHz(.M),andCHz(.M)
34
2.5
The pairing
CÌ^CM)
χ
CR1
(M)
-+
CK
(M)
36
2.6
Arakelov heights
38
2.7
The arithmetic adjunction formula
39
Bibliography
43
Chapter
3.
Cycles on Shimura curves
45
3.1
Shimura curves
46
3.2
Uniformization
47
3.3
The Hodge bundle
49
3.4
Special endomorphisms
51
3.5
Green functions
56
3.6
Special 0-cycles
57
Bibliography
68
Chapter
4.
An arithmetic theta function
71
4.1
The structure of arithmetic Chow groups
71
4.2
The arithmetic theta function
77
4.3
The vertical component: definite theta functions
79
4.4
The analytic component: Maass forms
87
4.5
The Mordell-Weil component
94
4.6
Borcherds' generating function
96
4.7
An intertwining property
100
Bibliography
102
Chapter
5.
The central derivative of a genus two
Eisenstein
series
105
5.1
Genus two
Eisenstein
series
105
5.2
Nonsingular Fourier coefficients
111
5.3
The Siegel-Weil formula
5.4
Singular coefficients
5.5
Eisenstein
series of genus one
5.6
Вт
5.7
Wt
5.8
The central derivative
—
the rank one case
5.9
The constant term
Bibliography
Vi
CONTENTS
121
137
139
140
144
154
161
165
Chapter
6.
The generating function for O-cycles
167
6.1
ThecaseT>OwithDiff(T,B) = {p}forp|I)(B)
169
6.2
The case
Τ
> 0
with Diff(T, B)
=
{p} for p\D(B)
172
6.3
The case of nonsingular
Τ
with sig(T)
= (1,1)
or
(0,2) 175
6.4
Singular terms,
Τ
of rank
1 177
6.5
The constant term,
Τ
= 0 179
Bibliography
180
Chapter
6
Appendix. The case p-2,p\ D(B)
181
6A.
1
Statement of the result
181
6A.2 Review of the special cycles Z(j), for q(j)
Є
Zp \
{0} 186
6A.3 Configurations
188
6A.4 Calculations
191
6A.5 The first
nondiagonal
case
201
Bibliography
204
Chapter
7.
An inner product formula
205
7.1
Statement of the main result
206
7.2
The case t\ti is not a square
208
7.3
A weakly admissible Green function
212
7.4
A finer decomposition of special cycles
221
7.5
Application of adjunction
225
7.6
Contributions for
ρ \
D(B)
231
7.7
Contributions for
p j D (B)
238
7.8
Computation of the discriminant terms
245
7.9
Comparison for the case ii, i2
> 0,
and M2
=
m2
252
7.10
The case tu i2
< 0
with tit2
=
m2
259
7.11
The constant terms
262
Bibliography
264
Chapter
8.
On the doubling integral
265
8.1
The global doubling integral
266
8.2
Review of Waldspurger's theory
269
8.3
An explicit doubling formula
279
8.4
Local doubling integrals
285
8.5
Appendix: Coordinates on metaplectic groups
320
Bibliography
346
CONTENTS
VU
Chapter
9.
Central derivatives of L-functions
351
9.1
The arithmetic theta lift
351
9.2
The arithmetic inner product formula
356
9.3
The relation with classical newforms
365
Bibliography
369
Index
371 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Kudla, Stephen S. 1950- Rapoport, Michael 1948- Yang, Tonghai 1963- |
| author_GND | (DE-588)139721665 (DE-588)140462945 (DE-588)140463003 |
| author_facet | Kudla, Stephen S. 1950- Rapoport, Michael 1948- Yang, Tonghai 1963- |
| author_role | aut aut aut |
| author_sort | Kudla, Stephen S. 1950- |
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| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.3 15 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV021645347 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T15:01:19Z |
| indexdate | 2024-07-09T20:40:41Z |
| institution | BVB |
| isbn | 0691125503 0691125511 9780691125503 9780691125510 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014860065 |
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| physical | vii, 373 Seiten |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Kudla, Stephen S. 1950- Verfasser (DE-588)139721665 aut Modular forms and special cycles on Shimura curves Stephen S. Kudla ; Michael Rapoport ; Tonghai Yang Princeton, NJ Princeton University Press 2006 © 2006 vii, 373 Seiten txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 161 Géométrie algébrique arithmétique Shimura, Variétés de Arithmetical algebraic geometry Shimura varieties Shimura-Kurve (DE-588)4705871-7 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf Eisenstein-Reihe (DE-588)4131762-2 gnd rswk-swf Thetafunktion (DE-588)4185175-4 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 s Shimura-Kurve (DE-588)4705871-7 s Thetafunktion (DE-588)4185175-4 s Eisenstein-Reihe (DE-588)4131762-2 s DE-604 Rapoport, Michael 1948- Verfasser (DE-588)140462945 aut Yang, Tonghai 1963- Verfasser (DE-588)140463003 aut Erscheint auch als Online-Ausgabe 978-1-4008-3716-8 Annals of mathematics studies number 161 (DE-604)BV000000991 161 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014860065&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kudla, Stephen S. 1950- Rapoport, Michael 1948- Yang, Tonghai 1963- Modular forms and special cycles on Shimura curves Annals of mathematics studies Géométrie algébrique arithmétique Shimura, Variétés de Arithmetical algebraic geometry Shimura varieties Shimura-Kurve (DE-588)4705871-7 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd Eisenstein-Reihe (DE-588)4131762-2 gnd Thetafunktion (DE-588)4185175-4 gnd |
| subject_GND | (DE-588)4705871-7 (DE-588)4131383-5 (DE-588)4131762-2 (DE-588)4185175-4 |
| title | Modular forms and special cycles on Shimura curves |
| title_auth | Modular forms and special cycles on Shimura curves |
| title_exact_search | Modular forms and special cycles on Shimura curves |
| title_exact_search_txtP | Modular forms and special cycles on Shimura curves |
| title_full | Modular forms and special cycles on Shimura curves Stephen S. Kudla ; Michael Rapoport ; Tonghai Yang |
| title_fullStr | Modular forms and special cycles on Shimura curves Stephen S. Kudla ; Michael Rapoport ; Tonghai Yang |
| title_full_unstemmed | Modular forms and special cycles on Shimura curves Stephen S. Kudla ; Michael Rapoport ; Tonghai Yang |
| title_short | Modular forms and special cycles on Shimura curves |
| title_sort | modular forms and special cycles on shimura curves |
| topic | Géométrie algébrique arithmétique Shimura, Variétés de Arithmetical algebraic geometry Shimura varieties Shimura-Kurve (DE-588)4705871-7 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd Eisenstein-Reihe (DE-588)4131762-2 gnd Thetafunktion (DE-588)4185175-4 gnd |
| topic_facet | Géométrie algébrique arithmétique Shimura, Variétés de Arithmetical algebraic geometry Shimura varieties Shimura-Kurve Arithmetische Geometrie Eisenstein-Reihe Thetafunktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014860065&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT kudlastephens modularformsandspecialcyclesonshimuracurves AT rapoportmichael modularformsandspecialcyclesonshimuracurves AT yangtonghai modularformsandspecialcyclesonshimuracurves |