Twisted L-functions and monodromy:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton and Oxford
Princeton University Press
2001
|
| Series: | Annals of mathematics studies
number 150 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | viii, 249 Seiten |
| ISBN: | 9780691091518 0691091501 069109151X |
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 Twisted L-functions and monodromy |c by Nicholas M. Katz |
| 264 | 1 | |a Princeton and Oxford |b Princeton University Press |c 2001 | |
| 264 | 4 | |c © 2001 | |
| 300 | |a viii, 249 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 150 | |
| 650 | 4 | |a Elliptische Kurve - L-Funktion - Monodromie | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a L-functions | |
| 650 | 4 | |a Monodromy groups | |
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| 650 | 0 | 7 | |a Monodromie |0 (DE-588)4277667-3 |2 gnd |9 rswk-swf |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Introduction 3
Part I: Background Material
Chapter 1: Abstract Theorems of Big Monodromy 23
1.0 Two generalizations of the notion of pseudoreflection 23
1.1 Basic Lemmas on elements of low drop 24
1.2 Tensor products and tameness at °° 26
1.3 Tensor indecomposability of sheaves whose local
monodromies have low drop 28
1.4 Monodromy groups in the Lie—irreducible case 30
1.5 Statement of the main technical result 35
1.6 Proof of Theorem 1.5.1 36
1.7 A sharpening of Theorem 1.5.1 when Rmjn = 1 or
when some local monodromy is a reflection 42
Appendix to Chapter 1: A Result of Zalesskii 43
Chapter 2: Lefschetz Pencils, Especially on Curves 51
2.0 Review of Lefschetz pencils [SGA 7, Expose XVII] 51
2.1 The dual variety in the favorable case 55
2.2 Lefschetz pencils on curves in characteristic not 2 58
2.3 The situation for curves in arbitrary characteristic 60
2.4 Lefschetz pencils on curves in characteristic 2 62
2.5 Comments on Theorem 2.4.4 63
2.6 Proof of Theorem 2.4.4 64
2.7 Application to Swan conductors in characteristic 2 69
Chapter 3: Induction 71
3.0 The two sorts of induction 71
3.1 Induction and duality 72
3.2 Induction as direct image 73
3.3 A criterion for the irreducibility of a direct image 74
3.4 Autoduality and induction 75
3.5 A criterion for being induced 76
vi Contents
Chapter 4: Middle Convolution 79
4.0 Review of middle additive convolution: the class !Pconv 79
4.1 Effect on local monodromy 80
4.2 Calculation of MC,loc(a) on certain wild characters 82
Part II. Twist Sheaves, over an Algebraically Closed Field
Chapter S: Twist Sheaves and Their Monodromy 85
5.0 Families of twists: basic definitions and constructions 85
5.1 Basic facts about the groups H (C, )*(T 8 £y,f )) 87
5.2 Putting together the groups H^C, j*CF®£y(f))) 89
5.3 First properties of twist families: relation to middle
additive convolution on A* 93
5.4 Theorems of big monodromy in characteristic not 2 98
5.5 Theorems of big monodromy for Q := Twisty q rj(!F)
on Fct(C, d, D, SingCf)fjnite) in characteristic not 2 109
5.6 Theorems of big monodromy in characteristic 2 112
5.7 Theorems of big monodromy for Q := Twists q yCF)
on Fct(C, d, D, Sing( F)fimte) in characteristic 2 115
Part DI: Twist Sheaves, over a Finite Field
Chapter 6: Dependence on Parameters 117
6.0 A lemma on relative Cartier divisors 117
6.1 The situation with curves 118
6.2 Construction of the twist sheaf Q := Twisty q rj(!F) with parameters 122
Chapter 7: Diophantine Applications over a Finite Reid 125
7.0 The general setup over a finite field: relation of
the sheaf Q := Twisty q rjCF) to L functions of twists 125
7.1 Applications to equidistribution 126
7.2 The SL case 127
7.3 The Sp case 128
7.4 The O or SO case 128
7.5 Interlude: a lemma on tameness and compatible systems 131
Contents vii
7.6 Applications to L functions of quadratic twists of elliptic
curves and of their symmetric powers over function fields 132
7.7 Applications to L functions of Prym varieties 135
7.8 Families of hyperelliptic curves as a special case 136
7.9 Application to L functions of ^ components of Jacobians
of cyclic coverings of degree n 3 in odd characteristic 136
7.10 Application to L functions of ^ components of Jacobians
of cyclic coverings of odd degree n 3 in characteristic 2 144
Chapter 8: Average Order of Zero in Twist Families 147
8.0 The basic setting 147
8.1 Definitions of three sorts of analytic rank 147
8.2 Relation to Mordell Weil rank 147
8.3 Theorems on average analytic ranks, and on average Mordell Weil rank 148
8.4 Examples of input Ts with small Ggeorn 155
8.5 Criteria for when Ggeom is SO rather than O 158
8.6 An interesting example 163
8.7 Proof of Theorem 8.6.5 164
8.8 Explicit determination of the representation Pga| ( 168
8.9 A family of interesting examples 172
8.10 Another family of examples 176
Part IV: Twist Sheaves, over Schemes of Finite Type over Z
Chapter 9: Twisting by Primes , and Working over Z 179
9.0 Construction of some Sj torsors 179
9.1 Theorems of geometric connectedness 182
9.2 Interpretation in terms of geometric monodromy groups 187
9.3 Relation to splitting of primes 188
9.4 Distribution of primes in the spaces Xt := Fct(Ct, d, Dt, St) 189
9.5 Equidistribution theorems for twists by primes:
the basic setup over a finite field 90
9.6 Equidistribution theorems for twists by primes:
uniformities with respect to parameters in the basic setup above 194
9.7 Applications of Goursat s Lemma 197
9.8 Interlude: detailed discussion of the 0(N)xSd case 198
9.9 Application to twist sheaves 99
9.10 Equidistribution theorems for twists by primes, over finite fields 201
|
| any_adam_object | 1 |
| author | Katz, Nicholas M. 1943- |
| author_GND | (DE-588)141265558 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 274 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014165477 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:58:51Z |
| institution | BVB |
| isbn | 9780691091518 0691091501 069109151X |
| language | English |
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| physical | viii, 249 Seiten |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Katz, Nicholas M. 1943- Verfasser (DE-588)141265558 aut Twisted L-functions and monodromy by Nicholas M. Katz Princeton and Oxford Princeton University Press 2001 © 2001 viii, 249 Seiten txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies number 150 Elliptische Kurve - L-Funktion - Monodromie Curves, Elliptic L-functions Monodromy groups L-Funktion (DE-588)4137026-0 gnd rswk-swf Monodromie (DE-588)4277667-3 gnd rswk-swf L-Funktion (DE-588)4137026-0 s Monodromie (DE-588)4277667-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4008-2488-5 Annals of mathematics studies number 150 (DE-604)BV000000991 150 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009709641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Katz, Nicholas M. 1943- Twisted L-functions and monodromy Annals of mathematics studies Elliptische Kurve - L-Funktion - Monodromie Curves, Elliptic L-functions Monodromy groups L-Funktion (DE-588)4137026-0 gnd Monodromie (DE-588)4277667-3 gnd |
| subject_GND | (DE-588)4137026-0 (DE-588)4277667-3 |
| title | Twisted L-functions and monodromy |
| title_auth | Twisted L-functions and monodromy |
| title_exact_search | Twisted L-functions and monodromy |
| title_full | Twisted L-functions and monodromy by Nicholas M. Katz |
| title_fullStr | Twisted L-functions and monodromy by Nicholas M. Katz |
| title_full_unstemmed | Twisted L-functions and monodromy by Nicholas M. Katz |
| title_short | Twisted L-functions and monodromy |
| title_sort | twisted l functions and monodromy |
| topic | Elliptische Kurve - L-Funktion - Monodromie Curves, Elliptic L-functions Monodromy groups L-Funktion (DE-588)4137026-0 gnd Monodromie (DE-588)4277667-3 gnd |
| topic_facet | Elliptische Kurve - L-Funktion - Monodromie Curves, Elliptic L-functions Monodromy groups L-Funktion Monodromie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009709641&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT katznicholasm twistedlfunctionsandmonodromy |