Moments, monodromy, and perversity: a diophantine perspective
It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions...
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| Sprache: | English |
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Princeton, NJ
Princeton University Press
[2005]
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| Schriftenreihe: | Annals of Mathematics Studies
number 159 |
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| Online-Zugang: | FAW01 FHA01 FKE01 FLA01 UPA01 FAB01 FCO01 Volltext |
| Zusammenfassung: | It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a "generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family. Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Moments, Monodromy, and Perversity, Nicholas Katz develops new techniques, which are resolutely global in nature. They are based on two vital ingredients, neither of which existed at the time of Deligne's original work on the subject. The first is the theory of perverse sheaves, pioneered by Goresky and MacPherson in the topological setting and then brilliantly transposed to algebraic geometry by Beilinson, Bernstein, Deligne, and Gabber. The second is Larsen's Alternative, which very nearly characterizes classical groups by their fourth moments. These new techniques, which are of great interest in their own right, are first developed and then used to calculate the geometric monodromy groups attached to some quite specific universal families of (L-functions attached to) character sums over finite fields |
| Beschreibung: | Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) |
| Beschreibung: | 1 online resource |
| ISBN: | 9781400826957 |
| DOI: | 10.1515/9781400826957 |
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| 520 | |a It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a "generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family. Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Moments, Monodromy, and Perversity, Nicholas Katz develops new techniques, which are resolutely global in nature. They are based on two vital ingredients, neither of which existed at the time of Deligne's original work on the subject. The first is the theory of perverse sheaves, pioneered by Goresky and MacPherson in the topological setting and then brilliantly transposed to algebraic geometry by Beilinson, Bernstein, Deligne, and Gabber. The second is Larsen's Alternative, which very nearly characterizes classical groups by their fourth moments. These new techniques, which are of great interest in their own right, are first developed and then used to calculate the geometric monodromy groups attached to some quite specific universal families of (L-functions attached to) character sums over finite fields | ||
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| discipline | Mathematik |
| doi_str_mv | 10.1515/9781400826957 |
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| spelling | Katz, Nicholas M. 1943- (DE-588)141265558 aut Moments, monodromy, and perversity a diophantine perspective Nicholas M. Katz Princeton, NJ Princeton University Press [2005] © 2005 1 online resource txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 159 Description based on online resource; title from PDF title page (publisher's Web site, viewed Jul. 04., 2016) It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably "pure" algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a "generalized Sato-Tate law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family. Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Moments, Monodromy, and Perversity, Nicholas Katz develops new techniques, which are resolutely global in nature. They are based on two vital ingredients, neither of which existed at the time of Deligne's original work on the subject. The first is the theory of perverse sheaves, pioneered by Goresky and MacPherson in the topological setting and then brilliantly transposed to algebraic geometry by Beilinson, Bernstein, Deligne, and Gabber. The second is Larsen's Alternative, which very nearly characterizes classical groups by their fourth moments. These new techniques, which are of great interest in their own right, are first developed and then used to calculate the geometric monodromy groups attached to some quite specific universal families of (L-functions attached to) character sums over finite fields In English L-functions Monodromy groups Sheaf theory Monodromiegruppe (DE-588)4194644-3 gnd rswk-swf L-Funktion (DE-588)4137026-0 gnd rswk-swf Garbentheorie (DE-588)4155956-3 gnd rswk-swf Monodromiegruppe (DE-588)4194644-3 s Garbentheorie (DE-588)4155956-3 s L-Funktion (DE-588)4137026-0 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 978-0-691-12329-5 Annals of Mathematics Studies number 159 (DE-604)BV040389493 159 https://doi.org/10.1515/9781400826957 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Katz, Nicholas M. 1943- Moments, monodromy, and perversity a diophantine perspective Annals of Mathematics Studies L-functions Monodromy groups Sheaf theory Monodromiegruppe (DE-588)4194644-3 gnd L-Funktion (DE-588)4137026-0 gnd Garbentheorie (DE-588)4155956-3 gnd |
| subject_GND | (DE-588)4194644-3 (DE-588)4137026-0 (DE-588)4155956-3 |
| title | Moments, monodromy, and perversity a diophantine perspective |
| title_auth | Moments, monodromy, and perversity a diophantine perspective |
| title_exact_search | Moments, monodromy, and perversity a diophantine perspective |
| title_full | Moments, monodromy, and perversity a diophantine perspective Nicholas M. Katz |
| title_fullStr | Moments, monodromy, and perversity a diophantine perspective Nicholas M. Katz |
| title_full_unstemmed | Moments, monodromy, and perversity a diophantine perspective Nicholas M. Katz |
| title_short | Moments, monodromy, and perversity |
| title_sort | moments monodromy and perversity a diophantine perspective |
| title_sub | a diophantine perspective |
| topic | L-functions Monodromy groups Sheaf theory Monodromiegruppe (DE-588)4194644-3 gnd L-Funktion (DE-588)4137026-0 gnd Garbentheorie (DE-588)4155956-3 gnd |
| topic_facet | L-functions Monodromy groups Sheaf theory Monodromiegruppe L-Funktion Garbentheorie |
| url | https://doi.org/10.1515/9781400826957 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT katznicholasm momentsmonodromyandperversityadiophantineperspective |