Twisted L-functions and monodromy:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
[2002]
|
| Schriftenreihe: | Annals of Mathematics Studies
number 150 |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Main description: For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry |
| Beschreibung: | 1 Online-Ressource (264 S.) |
| ISBN: | 9781400824885 |
| DOI: | 10.1515/9781400824885 |
Internformat
MARC
| LEADER | 00000nmm a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV042522165 | ||
| 003 | DE-604 | ||
| 005 | 20200331 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 150423s2002 |||| o||u| ||||||eng d | ||
| 020 | |a 9781400824885 |9 978-1-4008-2488-5 | ||
| 024 | 7 | |a 10.1515/9781400824885 |2 doi | |
| 035 | |a (OCoLC)1165608996 | ||
| 035 | |a (DE-599)BVBBV042522165 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-859 |a DE-860 |a DE-Aug4 |a DE-739 |a DE-1046 |a DE-83 |a DE-1043 |a DE-858 | ||
| 084 | |a SI 830 |0 (DE-625)143195: |2 rvk | ||
| 084 | |a SK 180 |0 (DE-625)143222: |2 rvk | ||
| 084 | |a SK 300 |0 (DE-625)143230: |2 rvk | ||
| 100 | 1 | |a Katz, Nicholas M. |d 1943- |0 (DE-588)141265558 |4 aut | |
| 245 | 1 | 0 | |a Twisted L-functions and monodromy |
| 264 | 1 | |a Princeton, N.J. |b Princeton University Press |c [2002] | |
| 264 | 4 | |c © 2002 | |
| 300 | |a 1 Online-Ressource (264 S.) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 1 | |a Annals of Mathematics Studies |v number 150 | |
| 500 | |a Main description: For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry | ||
| 650 | 0 | 7 | |a Monodromie |0 (DE-588)4277667-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a L-Funktion |0 (DE-588)4137026-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a L-Funktion |0 (DE-588)4137026-0 |D s |
| 689 | 0 | 1 | |a Monodromie |0 (DE-588)4277667-3 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 978-0-691-09150-1 |
| 830 | 0 | |a Annals of Mathematics Studies |v number 150 |w (DE-604)BV040389493 |9 150 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400824885?locatt=mode:legacy |x Verlag |z URL des Erstveröffentlichers |3 Volltext |
| 856 | 4 | 0 | |u http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400824885&searchTitles=true |x Verlag |3 Volltext |
| 912 | |a ZDB-23-DGG |a ZDB-23-PST | ||
| 940 | 1 | |q FKE_PDA_DGG | |
| 940 | 1 | |q FLA_PDA_DGG | |
| 940 | 1 | |q FHA_PDA_DGG | |
| 940 | 1 | |q UPA_PDA_DGG | |
| 940 | 1 | |q FAW_PDA_DGG | |
| 940 | 1 | |q FCO_PDA_DGG | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027956504 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
Datensatz im Suchindex
| _version_ | 1804153274642726912 |
|---|---|
| any_adam_object | |
| 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 | BV042522165 |
| classification_rvk | SI 830 SK 180 SK 300 |
| collection | ZDB-23-DGG ZDB-23-PST |
| ctrlnum | (OCoLC)1165608996 (DE-599)BVBBV042522165 |
| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400824885 |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03404nmm a2200541 cb4500</leader><controlfield tag="001">BV042522165</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200331 </controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">150423s2002 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400824885</subfield><subfield code="9">978-1-4008-2488-5</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400824885</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1165608996</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV042522165</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-859</subfield><subfield code="a">DE-860</subfield><subfield code="a">DE-Aug4</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-1046</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-1043</subfield><subfield code="a">DE-858</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SI 830</subfield><subfield code="0">(DE-625)143195:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 180</subfield><subfield code="0">(DE-625)143222:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 300</subfield><subfield code="0">(DE-625)143230:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Katz, Nicholas M.</subfield><subfield code="d">1943-</subfield><subfield code="0">(DE-588)141265558</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Twisted L-functions and monodromy</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, N.J.</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">[2002]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2002</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (264 S.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Annals of Mathematics Studies</subfield><subfield code="v">number 150</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Main description: For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Monodromie</subfield><subfield code="0">(DE-588)4277667-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">L-Funktion</subfield><subfield code="0">(DE-588)4137026-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">L-Funktion</subfield><subfield code="0">(DE-588)4137026-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Monodromie</subfield><subfield code="0">(DE-588)4277667-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">978-0-691-09150-1</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Annals of Mathematics Studies</subfield><subfield code="v">number 150</subfield><subfield code="w">(DE-604)BV040389493</subfield><subfield code="9">150</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400824885?locatt=mode:legacy</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveröffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400824885&searchTitles=true</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-DGG</subfield><subfield code="a">ZDB-23-PST</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FKE_PDA_DGG</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FLA_PDA_DGG</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FHA_PDA_DGG</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">UPA_PDA_DGG</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FAW_PDA_DGG</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="q">FCO_PDA_DGG</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-027956504</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield></record></collection> |
| id | DE-604.BV042522165 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:24:00Z |
| institution | BVB |
| isbn | 9781400824885 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027956504 |
| oclc_num | 1165608996 |
| open_access_boolean | |
| owner | DE-859 DE-860 DE-Aug4 DE-739 DE-1046 DE-83 DE-1043 DE-858 |
| owner_facet | DE-859 DE-860 DE-Aug4 DE-739 DE-1046 DE-83 DE-1043 DE-858 |
| physical | 1 Online-Ressource (264 S.) |
| psigel | ZDB-23-DGG ZDB-23-PST FKE_PDA_DGG FLA_PDA_DGG FHA_PDA_DGG UPA_PDA_DGG FAW_PDA_DGG FCO_PDA_DGG |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Princeton University Press |
| record_format | marc |
| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Katz, Nicholas M. 1943- (DE-588)141265558 aut Twisted L-functions and monodromy Princeton, N.J. Princeton University Press [2002] © 2002 1 Online-Ressource (264 S.) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 150 Main description: For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry Monodromie (DE-588)4277667-3 gnd rswk-swf L-Funktion (DE-588)4137026-0 gnd rswk-swf L-Funktion (DE-588)4137026-0 s Monodromie (DE-588)4277667-3 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-691-09150-1 Annals of Mathematics Studies number 150 (DE-604)BV040389493 150 https://doi.org/10.1515/9781400824885?locatt=mode:legacy Verlag URL des Erstveröffentlichers Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400824885&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Katz, Nicholas M. 1943- Twisted L-functions and monodromy Annals of Mathematics Studies Monodromie (DE-588)4277667-3 gnd L-Funktion (DE-588)4137026-0 gnd |
| subject_GND | (DE-588)4277667-3 (DE-588)4137026-0 |
| 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 |
| title_fullStr | Twisted L-functions and monodromy |
| title_full_unstemmed | Twisted L-functions and monodromy |
| title_short | Twisted L-functions and monodromy |
| title_sort | twisted l functions and monodromy |
| topic | Monodromie (DE-588)4277667-3 gnd L-Funktion (DE-588)4137026-0 gnd |
| topic_facet | Monodromie L-Funktion |
| url | https://doi.org/10.1515/9781400824885?locatt=mode:legacy http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400824885&searchTitles=true |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT katznicholasm twistedlfunctionsandmonodromy |