Gauss sums, Kloosterman sums, and monodromy groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
1988
|
| Series: | Annals of mathematics studies
116 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 246 S. |
| ISBN: | 0691084327 0691084335 |
Staff View
MARC
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| 100 | 1 | |a Katz, Nicholas M. |d 1943- |e Verfasser |0 (DE-588)141265558 |4 aut | |
| 245 | 1 | 0 | |a Gauss sums, Kloosterman sums, and monodromy groups |c by Nicholas M. Katz |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 1988 | |
| 300 | |a VIII, 246 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Annals of mathematics studies |v 116 | |
| 650 | 7 | |a Gauss, sommes de |2 ram | |
| 650 | 7 | |a Groupes de monodromie |2 ram | |
| 650 | 7 | |a Homologie |2 ram | |
| 650 | 7 | |a Kloosterman, sommes de |2 ram | |
| 650 | 4 | |a Gaussian sums | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Kloosterman sums | |
| 650 | 4 | |a Monodromy groups | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 1
Chapter 1. Breaks and Swan Conductors 12
1.0 The basic setting 12
1.1 1.10 Definitions and basic properties of breaks, break
decompositions, and Swan conductors 12
1.11 1.17 Representation theoretic consequences of particular arrays
of breaks 17
1.18 1.20 Detailed analysis when Swan =1 23
Chapter 2. Curves and Their Cohomology 26
2.0 Generalities 26
2.1 Cohomology of wild sheaves 28
2.2 Canonical calculations of cohomology 28
2.3 The Euler Poincare and Lefschetz trace formulas 31
Chapter 3. Equidistribution in Equal Characteristic 36
3.0 3.5 The basic setting 36
3.6 The equidistribution theorem 38
3.7 Remark on the integration of sufficiently smooth functions 42
Chapter 4. Gauss Sums and Kloosterman Sums: Kloosterman
Sheaves 46
4.0 Kloosterman sums as inverse Fourier transforms of mono¬
mials in Gauss sums 46
4.1 The existence theorem for Kloosterman sheaves 48
4.2 Signs of pairings 54
4.3 The existence theorem for n — 1, via the sheaves C,p and
Cx 59
vi Contents
Chapter 5. Convolution of Sheaves on Gm 62
5.0 The basic setting, and a lemma 62
5.1 Statement of the convolution theorem 63
5.2 Proof of the convolution theorem and variations 65
5.3 Convolution and duality: Signs 77
5.4 Multiple convolution 79
5.5 First applications to Kloosterman sheaves 80
5.6 Direct images of Kloosterman sheaves, via Hasse
Davenport 84
Chapter 6. Local Convolution 87
6.0 Formulation of the problem 87
6.1 Consequences of a solution 87
6.2 6.4 Preparations 88
6.5 A theorem on vanishing cycles 90
6.6 Construction of local convolution 95
Chapter 7. Local Monodromy at Zero of a Convolution:
Detailed Study 96
7.0 General review of local monodromy 96
7.1 Application to a product formula for a convolution
of pure sheaves 100
7.2 Application to sheaves with Swanoo = 1 104
7.3 Application to Kloosterman sheaves 105
7.4 Some special cases 107
7.5 Appendix: The product formula in the general case
(d apres O. Gabber) 109
7.6 Appendix: An open problem concerning breaks of
a convolution 117
Chapter 8. Complements on Convolution 120
8.0 A cancellation theorem for convolution 120
8.1 Two variants of the cancellation theorem 127
8.2 Interlude: Naive Fourier transform 130
8.3 Basic examples of Fourier sheaves 134
8.4 Irreducible Fourier sheaves 135
8.5 Numerology of Fourier transform 136
8.6 Convolution with £^ as Fourier transform 142
I
Contents vii
8.7 Ubiquity of Kloosterman sheaves 146
8.8 The structure over Fq: Canonical descents of
Kloosterman sheaves 148
I 8.9 Embedding in a compatible system 152
Chapter 9. Equidistribution in (S1)1 of r tuples of Angles
of Gauss Sums 155
i 9.0 Motivation: Davenport s theorem on consecutive
I quadratic residues 155
• 9.1 9.2 Formulation of the problem 157
9.3 9.5 The theorem, a reformulation, and a reduction 158
9.7 The end of the proof 165
, 9.8 Remark concerning the proof 166
Chapter 10. Local Monodromy at oo of Kloosterman
Sheaves 168
10.0 Review of some independence of / results 168
10.1 Independence of / and x s as Poo representation 168
10.2 Independence of / and x s of oo breaks of tensor
products 169
10.3 10.4 Breaks and Swans of tensor products 169
Chapter 11. Global Monodromy of Kloosterman Sheaves 176
11.0 Formulation of the theorem 176
11.1 Statement of the main theorem 178
11.2 Remarks and comments 179
11.3 A corollary 179
11.4 First application to equidistribution 180
11.5 Axiomatics of the proof; classification theorems 180
11.6 The classification theorem 184
11.7 An axiomatic classification theorem 185
11.8 G2 Theorem 186
11.9 Density Theorem 186
11.10 Proof of the classification theorem (11.6) 186
11.11 Proof of the G2 Theorem 200
viii Contents
Chapter 12. Integral Monodromy of Kloosterman Sheaves
(d apres O. Gabber) 210
12.0 Formulation of the theorem 210
12.1 The theorem 211
12.2 A more precise version 212
12.3 Reduction to a universal situation 212
12.4 Generation by unipotent elements 217
12.5 Analysis of the special case p = 2, n odd ^ 7 227
12.6 Analysis of the special case p = 2, n = 7 229
Chapter 13. Equidistibution of Angles of Kloosterman
Sums 234
13.0 13.4 Uniform description of the space of conjugacy classes
and its Haar measure 234
13.5 Formulation of the theorem 238
13.6 Example: the simplest case 240
References 243
|
| any_adam_object | 1 |
| author | Katz, Nicholas M. 1943- |
| author_GND | (DE-588)141265558 |
| author_facet | Katz, Nicholas M. 1943- |
| author_role | aut |
| author_sort | Katz, Nicholas M. 1943- |
| author_variant | n m k nm nmk |
| building | Verbundindex |
| bvnumber | BV002493349 |
| callnumber-first | Q - Science |
| callnumber-label | QA246 |
| callnumber-raw | QA246.8.G38 |
| callnumber-search | QA246.8.G38 |
| callnumber-sort | QA 3246.8 G38 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 830 SK 240 |
| ctrlnum | (OCoLC)16716978 (DE-599)BVBBV002493349 |
| dewey-full | 512/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.7 |
| dewey-search | 512/.7 |
| dewey-sort | 3512 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002493349 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:45:51Z |
| institution | BVB |
| isbn | 0691084327 0691084335 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001606375 |
| oclc_num | 16716978 |
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| physical | VIII, 246 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Katz, Nicholas M. 1943- Verfasser (DE-588)141265558 aut Gauss sums, Kloosterman sums, and monodromy groups by Nicholas M. Katz Princeton, NJ Princeton Univ. Press 1988 VIII, 246 S. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 116 Gauss, sommes de ram Groupes de monodromie ram Homologie ram Kloosterman, sommes de ram Gaussian sums Homology theory Kloosterman sums Monodromy groups Kloosterman-Summe (DE-588)4309220-2 gnd rswk-swf Monodromiegruppe (DE-588)4194644-3 gnd rswk-swf Gauß-Summe (DE-588)4156109-0 gnd rswk-swf Kloosterman-Summe (DE-588)4309220-2 s Monodromiegruppe (DE-588)4194644-3 s DE-604 Gauß-Summe (DE-588)4156109-0 s Annals of mathematics studies 116 (DE-604)BV000000991 116 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001606375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katz, Nicholas M. 1943- Gauss sums, Kloosterman sums, and monodromy groups Annals of mathematics studies Gauss, sommes de ram Groupes de monodromie ram Homologie ram Kloosterman, sommes de ram Gaussian sums Homology theory Kloosterman sums Monodromy groups Kloosterman-Summe (DE-588)4309220-2 gnd Monodromiegruppe (DE-588)4194644-3 gnd Gauß-Summe (DE-588)4156109-0 gnd |
| subject_GND | (DE-588)4309220-2 (DE-588)4194644-3 (DE-588)4156109-0 |
| title | Gauss sums, Kloosterman sums, and monodromy groups |
| title_auth | Gauss sums, Kloosterman sums, and monodromy groups |
| title_exact_search | Gauss sums, Kloosterman sums, and monodromy groups |
| title_full | Gauss sums, Kloosterman sums, and monodromy groups by Nicholas M. Katz |
| title_fullStr | Gauss sums, Kloosterman sums, and monodromy groups by Nicholas M. Katz |
| title_full_unstemmed | Gauss sums, Kloosterman sums, and monodromy groups by Nicholas M. Katz |
| title_short | Gauss sums, Kloosterman sums, and monodromy groups |
| title_sort | gauss sums kloosterman sums and monodromy groups |
| topic | Gauss, sommes de ram Groupes de monodromie ram Homologie ram Kloosterman, sommes de ram Gaussian sums Homology theory Kloosterman sums Monodromy groups Kloosterman-Summe (DE-588)4309220-2 gnd Monodromiegruppe (DE-588)4194644-3 gnd Gauß-Summe (DE-588)4156109-0 gnd |
| topic_facet | Gauss, sommes de Groupes de monodromie Homologie Kloosterman, sommes de Gaussian sums Homology theory Kloosterman sums Monodromy groups Kloosterman-Summe Monodromiegruppe Gauß-Summe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001606375&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT katznicholasm gausssumskloostermansumsandmonodromygroups |