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Research talks;Algebraic and Complex Geometry;Number Theory

The $p$-adic Igusa zeta function, topological and motivic zeta function are (related) invariants of a polynomial $f$, reflecting the singularities of the hypersurface $f = 0$. The first one has a number theoretical flavor and is related to counting numbers of solutions of $f = 0$ over finite rings; the other two are more geometric in nature. The monodromy conjecture relates in a mysterious way these invariants to another singularity invariant of $f$, its local monodromy. We will discuss in this survey talk rationality issues for these zeta functions and the origins of the conjecture. The $p$-adic Igusa zeta function, topological and motivic zeta function are (related) invariants of a polynomial $f$, reflecting the singularities of the hypersurface $f = 0$. The first one has a number theoretical flavor and is related to counting numbers of solutions of $f = 0$ over finite rings; the other two are more geometric in nature. The monodromy conjecture relates in a mysterious way these invariants to another singularity invariant of ...

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Documents 14D05 | enregistrements trouvés : 38

Zeta functions and monodromy Veys, Wim | CIRM H Nouveau

Séminaire Bourbaki. Vol. 1992/93 :exposés 760-774 | Société Mathématique de France 1993 Nouveau

Séminaire Bourbaki. Vol. 1974/75exposés 453-470 Bourbaki, N. | Springer-Verlag 1976 Nouveau

Singularités Franco-Japonaise#Sept. 9-13 Brasselet, Jean-Paul ; Suwa, Tatsuo | Société Mathématique de France 2005 Nouveau

Singularities in geometry and topology#Sept. 13-18 Brasselet, Jean-Paul ; Suwa, Tatsuo | Mathematical Society of Japan 2007 Nouveau

Séminaire de géométrie algébrique du Bois Marie 1967-69 SGA 7 IIgroupes de monodromie en géométrie algébrique Deligne, P. ; Katz, N. | Springer-Verlag 1973 Nouveau

Groupes de monodromie en géométrie algébriqueséminaire de géométrie algébrique du Bois-Marie 1967-1969 Grothendieck, A. ; Raynaud, M. ; Rim, D. S. | Springer-Verlag 1972 Nouveau

Minimal models and extremal rays.Proceedings of the conferenceKyoto # June 20-24, 2011 Kollár, János ; Fujino, Osamu ; Mukai, Shigeru ; Nakayama, Noboru | Mathematical Society of Japan 2016 Nouveau

Algebraic geometryproceedings of the midwest algebraic geometry conference was held at the university of illinois at chicago circle,may 2-3,1980 Libgober, A. ; Wagreich, P. | Springer-Verlag 1981 Nouveau

Séminaire d'algèbre Paul Dubreil et Marie-Paule MalliavinproceedingsParis 1986 Malliavin, M. P. | Springer-Verlag 1987 Nouveau

Monodromy in problems of algebraic geometry and differential equations Mishchenko, Evgenii F. | MAIK Nauka/Interperiodica Publishing 2002 Nouveau

Higher dimensional algebraic geometry : in honour of Professor Yujiro Kawamata's 60th birthdayTokyo # January 7-11, 2013 Oguiso, Keiji ; Birkar, Caucher ; Ishii, Shihoko ; Takayama, Shigeharu | Mathematical Society of Japan 2017 Nouveau

Algebraic geometry 2000, Azumino#July 20-30 Usui, Sampei ; Green, Mark ; Illusie, Luc ; Kato, Kazuya | Mathematical Society of Japan 2002 Nouveau

Liverpool singularities symposium II :proceedings of Liverpool singularities symposium II held atthe university of Liverpool#Sept.1969 - Aug. 1970 Wall, C. T. C. | Springer-Verlag 1971 Nouveau

Proceedings of Liverpool singularities symposium IISept. 1969 - Aug. 1970 Wall, C. T. C. | Springer-Verlag 1971 Nouveau

$D$-modules and $p$-curvatures Esnault, Hélène | CIRM H Nouveau

Cohomologies p-adiques et applications arithmétiques. Vol. II Berthelot, Pierre ; Fontaine, Jean-Marc ; Illusie, Luc ; Kato, Kazuya ; Rapoport, Michael | Société Mathématique de France 2002 Nouveau

Variétés rationnellement connexes: aspects géométriques et arithmétiques Bonavero, Laurent ; Hassett, Brendan ; Starr, Jason M. ; Wittenberg, Olivier ; Colliot-Thelene, J. L. | Société Mathématique de France 2010 Nouveau

Igusa's p-adic local zeta function and the monodromy conjecture for non-degenerate surface singularities Bories, Bart ; Veys, Willem | American Mathematical Society 2016 Nouveau

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Séminaire Bourbaki. Vol. 1992/93 :
exposés 760-774 | Société Mathématique de France 1993 Nouveau

Séminaire Bourbaki. Vol. 1974/75
exposés 453-470 Bourbaki, N. | Springer-Verlag 1976 Nouveau

Séminaire de géométrie algébrique du Bois Marie 1967-69 SGA 7 II
groupes de monodromie en géométrie algébrique Deligne, P. ; Katz, N. | Springer-Verlag 1973 Nouveau

Groupes de monodromie en géométrie algébrique
séminaire de géométrie algébrique du Bois-Marie 1967-1969 Grothendieck, A. ; Raynaud, M. ; Rim, D. S. | Springer-Verlag 1972 Nouveau

Minimal models and extremal rays.
Proceedings of the conference
Kyoto # June 20-24, 2011 Kollár, János ; Fujino, Osamu ; Mukai, Shigeru ; Nakayama, Noboru | Mathematical Society of Japan 2016 Nouveau

Algebraic geometry
proceedings of the midwest algebraic geometry conference was held at the university of illinois at chicago circle,may 2-3,1980 Libgober, A. ; Wagreich, P. | Springer-Verlag 1981 Nouveau

Séminaire d'algèbre Paul Dubreil et Marie-Paule Malliavin
proceedings
Paris 1986 Malliavin, M. P. | Springer-Verlag 1987 Nouveau

Higher dimensional algebraic geometry : in honour of Professor Yujiro Kawamata's 60th birthday
Tokyo # January 7-11, 2013 Oguiso, Keiji ; Birkar, Caucher ; Ishii, Shihoko ; Takayama, Shigeharu | Mathematical Society of Japan 2017 Nouveau

Liverpool singularities symposium II :
proceedings of Liverpool singularities symposium II held atthe university of Liverpool#Sept.1969 - Aug. 1970 Wall, C. T. C. | Springer-Verlag 1971 Nouveau

Proceedings of Liverpool singularities symposium II
Sept. 1969 - Aug. 1970 Wall, C. T. C. | Springer-Verlag 1971 Nouveau