Integration of one-forms on P-adic analytic spaces
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| Format: | Buch |
| Sprache: | English |
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Princeton and Oxford
Princeton University Press
2007
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| Schriftenreihe: | Annals of mathematics studies
number 162 |
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| 100 | 1 | |a Berkovič, Vladimir G. |e Verfasser |0 (DE-588)1157343074 |4 aut | |
| 245 | 1 | 0 | |a Integration of one-forms on P-adic analytic spaces |c Vladimir G. Berkovich |
| 264 | 1 | |a Princeton and Oxford |b Princeton University Press |c 2007 | |
| 264 | 4 | |c © 2007 | |
| 300 | |a vi, 156 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 162 | |
| 650 | 4 | |a Analytischer Raum - Integration <Mathematik> - DeRham-Komplex | |
| 650 | 4 | |a Analyse p-adique | |
| 650 | 4 | |a p-adic analysis | |
| 650 | 0 | 7 | |a Differentialform |0 (DE-588)4149772-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytischer Raum |0 (DE-588)4001871-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Integration |g Mathematik |0 (DE-588)4072852-3 |D s |
| 689 | 0 | 2 | |a Differentialform |0 (DE-588)4149772-7 |D s |
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| 830 | 0 | |a Annals of mathematics studies |v number 162 |w (DE-604)BV000000991 |9 162 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-015472630 | |
Datensatz im Suchindex
| DE-19_call_number | 1601/SI 830-162 |
|---|---|
| DE-19_location | 95 |
| DE-BY-TUM_call_number | 0102 MAT 144f 2012 A 4572 |
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| DE-BY-UBM_katkey | 3326538 |
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| _version_ | 1823053381411799040 |
| adam_text | Contents
Introduction 1
1. Naive Analytic Functions and Formulation of the Main Result 7
1.1 Preliminary remarks and notation 7
1.2 The sheaf of naive analytic functions 9
1.3 ©^ modules and £)^~modules 10
1.4 Logarithms 14
1.5 Logarithmic Poincare lemma 17
1.6 Formulation of the main results 20
2. Etale Neighborhoods of a Point in a Smooth Analytic Space 23
2.1 Etale neighborhoods of a point with s(x) = dim(X) 23
2.2 The local structure of a smooth analytic curve 28
2.3 Etale neighborhoods of a point with s(x) dim(X) 32
2.4 Basic curves 35
3. Properties of Strictly Poly stable and Marked Formal Schemes 39
3.1 Strictly poly stable formal schemes 39
3.2 Open neighborhoods of the generic point of an irreducible component 43
3.3 A property of strata 47
3.4 A tubular neighborhood of the diagonal of a stratum closure 48
3.5 The same for proper marked formal schemes 51
4. Properties of the Sheaves Q^d/dOx 55
4.1 Analytic curve connectedness of closed analytic spaces 55
4.2 The sheaves O°x, Ox, and O 57
4.3 Structure of the sheaves Sl /dOx for smooth analytic curves 59
4.4 Injectivity of the homomorphism rfLog : O ®z cx » ttxd/dOx 63
4.5 Asubsheaf *^ c n^ /^Ojc and a subspace Vx,x cQxdJdOXx 65
5. Isocrystals 71
5.1 Wide germs of analytic spaces and of formal schemes 71
5.2 © modules on smooth strictly £ affinoid germs and isocrystals 74
5.3 A construction of isocrystals 78
5.4 The filtered isocrystals Eg and the shuffle algebras 81
5.5 Unipotent isocrystals E (X, 3) 83
Vi CONTENTS
6. F isocrystals 87
6. J Frobenius liftings 87
6.2 A Frobenius structure on the isocrystals E (X, 3) 88
6.3 A uniqueness property of certain F isocrystals 89
6.4 Structure of a commutative filtered £ s algebra on E{X, 3) 91
6.5 Filtered F isocrystals EK(X, 3) and Tk(X, 3) 92
7. Construction of the Sheaves S$ 95
7.1 Induction hypotheses 95
7.2 Split one forms 98
7.3 Marked and weakly marked one forms 99
7.4 Construction of a primitive of a weakly marked one form 102
7.5 Construction of the XVmodules Sx +l 105
7.6 End of the proof 108
8. Properties of the sheaves S% 113
8.1 Filtered D(xrralgebras£x(X,Y) for germs with good reduction 114
8.2 Filtered Dxn algebras £X(X) for proper marked formal schemes 117
8.3 A filtered A^ subalgebrafj^ cSXx and the space Vx,x 119
8.4 More uniqueness properties 124
8.5 A filtered XVsubalgebra SxcSx and the sheaf •i x 127
9. Integration and Parallel Transport along a Path 131
9.1 Integration of closed one forms along a path 131
9.2 Nontrivial dependence on the homotopy class of a path 134
9.3 Locally unipotent and quasi unipotent X^y modules 136
9.4 Parallel transport along a path 139
9.5 Parallel transport along an etale path 144
References 149
Index of Notation 153
Index of Terminology 155
|
| any_adam_object | 1 |
| author | Berkovič, Vladimir G. |
| author_GND | (DE-588)1157343074 |
| author_facet | Berkovič, Vladimir G. |
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| author_sort | Berkovič, Vladimir G. |
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| bvnumber | BV022262003 |
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| callnumber-raw | QA241 |
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| dewey-full | 512.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.74 |
| dewey-search | 512.74 |
| dewey-sort | 3512.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV022262003 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-03T16:57:40Z |
| institution | BVB |
| isbn | 0691127417 0691128626 9780691127415 9780691128627 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015472630 |
| oclc_num | 255469455 |
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| physical | vi, 156 Seiten |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spellingShingle | Berkovič, Vladimir G. Integration of one-forms on P-adic analytic spaces Annals of mathematics studies Analytischer Raum - Integration <Mathematik> - DeRham-Komplex Analyse p-adique p-adic analysis Differentialform (DE-588)4149772-7 gnd Analytischer Raum (DE-588)4001871-4 gnd Integration Mathematik (DE-588)4072852-3 gnd |
| subject_GND | (DE-588)4149772-7 (DE-588)4001871-4 (DE-588)4072852-3 |
| title | Integration of one-forms on P-adic analytic spaces |
| title_auth | Integration of one-forms on P-adic analytic spaces |
| title_exact_search | Integration of one-forms on P-adic analytic spaces |
| title_full | Integration of one-forms on P-adic analytic spaces Vladimir G. Berkovich |
| title_fullStr | Integration of one-forms on P-adic analytic spaces Vladimir G. Berkovich |
| title_full_unstemmed | Integration of one-forms on P-adic analytic spaces Vladimir G. Berkovich |
| title_short | Integration of one-forms on P-adic analytic spaces |
| title_sort | integration of one forms on p adic analytic spaces |
| topic | Analytischer Raum - Integration <Mathematik> - DeRham-Komplex Analyse p-adique p-adic analysis Differentialform (DE-588)4149772-7 gnd Analytischer Raum (DE-588)4001871-4 gnd Integration Mathematik (DE-588)4072852-3 gnd |
| topic_facet | Analytischer Raum - Integration <Mathematik> - DeRham-Komplex Analyse p-adique p-adic analysis Differentialform Analytischer Raum Integration Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015472630&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT berkovicvladimirg integrationofoneformsonpadicanalyticspaces |