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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 14J17 | enregistrements trouvés : 47

Zeta functions and monodromy Veys, Wim | CIRM H Nouveau

Valuation theory in interaction.Proceedings of the 2nd international conference and workshop on valuation theorySegovia and El Escorial # July 18-29, 2011 Campillo, Antonio ; Kuhlmann, Franz-Viktor ; Teissier, Bernard | European Mathematical Society 2014 Nouveau

Topics in algebraic and noncommutative geometry :proceedings in memory of Ruth Michler held at CIRM#Luminy#July 20-22#Oct. 25-28 Melles, Caroline Grant ; Brasselet, Jean-Paul ; Kennedy, Gary ; Lauter, Kristin | American Mathematical Society 2003 Nouveau

Singularities in geometry, topology, foliations and dynamics:a celebration of the 60th birthday of José SeadeMérida # December 8-19, 2014 Cisneros-Molina, José Luis ; Tráng Lê, Dũng ; Oka, Mutsuo ; Snoussi, Jawad | Birkhäuser 2017 Nouveau

Singularities in geometry and topology:Strasbourg 2009Proceedings of the 5th Franco-Japanese symposium on singularitiesStrasbourg # august 24-28, 2009 Blanloeil, Vincent ; Ohmoto, Toru | European Mathematical Society 2012 Nouveau

Singularities in geometry and topology 2011.Proceedings of the 6th Franco-Japanese symposium on singularitiesFukuoka # September 5-10, 2011 Blanloeil, Vincent ; Saeki, Osamu | Mathematical Society of Japan 2015 Nouveau

Singularities : Niigata-Toyama 2007 Brasselet, Jean-Paul ; Ishii, Shihoko ; Suwa, Tatsuo ; Vaquie, Michel | Mathematical Society of Japan 2009 Nouveau

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

Séminaire sur les singularités des surfaces :Centre de Mathématiques de l'Ecole Polytechnique 1976-1977 Demazure, M. ; Pinkham, H. ; Teissier, B. | Springer 1980 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

Geometry of singularities and manifoldproceedings of the conferenceKusatsu # september 12-16, 2008 Ashikaga, Tadashi ; Konno, Kazuhiro ; Tomaru, Tadashi ; Usui, Sampei | Kusatsu seminar house;the grants-in-aid for scientific research 2009 Nouveau

Contributions to algebraic geometry:Impanga lecture notes.Based on the Impanga conference on algebraic geometryBedlewo # july 4-10, 2010 Pragacz, Piotr | European Mathematical Society 2012 Nouveau

Arithmetical algebraic geometryproceedings of a conference held at Purdue University Dec. 5-7 Schilling, O. F. G. | Harper & Row, Publishers 1965 Nouveau

Algebriac geometry :proceedings of the 3rd midwest conference on... held at the university of michigan#Nov. 14-15 Dolgachev, I. | Springer-Verlag 1983 Nouveau

Algebraic in east asia Konno, Kazuhiro ; Nguyen-Khac, Viet | Mathematical Society of Japan 2008 Nouveau

Algebraic geometry in East Asia - Seoul 2008Proceedings of the 3rd international conference Seoul # november 11-15, 2008 Keum, JongHae ; Kondo, Shigeyuki ; Konno, Kazuhiro ; Oguiso, Keiji | Mathematical Society of Japan 2010 Nouveau

Actes du colloque de théorie de Hodge :Luminy#Juin 1 - 6 | Société Mathématique de France 1989 Nouveau

Vector Fields on Singular Varieties Brasselet, Jean-Paul ; Seade, José ; Suwa, Tatsuo | Springer 2009 Nouveau

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Valuation theory in interaction.
Proceedings of the 2nd international conference and workshop on valuation theory
Segovia and El Escorial # July 18-29, 2011 Campillo, Antonio ; Kuhlmann, Franz-Viktor ; Teissier, Bernard | European Mathematical Society 2014 Nouveau

Topics in algebraic and noncommutative geometry :
proceedings in memory of Ruth Michler held at CIRM#Luminy#July 20-22#Oct. 25-28 Melles, Caroline Grant ; Brasselet, Jean-Paul ; Kennedy, Gary ; Lauter, Kristin | American Mathematical Society 2003 Nouveau

Singularities in geometry, topology, foliations and dynamics:
a celebration of the 60th birthday of José Seade
Mérida # December 8-19, 2014 Cisneros-Molina, José Luis ; Tráng Lê, Dũng ; Oka, Mutsuo ; Snoussi, Jawad | Birkhäuser 2017 Nouveau

Singularities in geometry and topology:
Strasbourg 2009
Proceedings of the 5th Franco-Japanese symposium on singularities
Strasbourg # august 24-28, 2009 Blanloeil, Vincent ; Ohmoto, Toru | European Mathematical Society 2012 Nouveau

Singularities in geometry and topology 2011.
Proceedings of the 6th Franco-Japanese symposium on singularities
Fukuoka # September 5-10, 2011 Blanloeil, Vincent ; Saeki, Osamu | Mathematical Society of Japan 2015 Nouveau

Séminaire sur les singularités des surfaces :
Centre de Mathématiques de l'Ecole Polytechnique 1976-1977 Demazure, M. ; Pinkham, H. ; Teissier, B. | Springer 1980 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

Geometry of singularities and manifold
proceedings of the conference
Kusatsu # september 12-16, 2008 Ashikaga, Tadashi ; Konno, Kazuhiro ; Tomaru, Tadashi ; Usui, Sampei | Kusatsu seminar house;the grants-in-aid for scientific research 2009 Nouveau

Contributions to algebraic geometry:
Impanga lecture notes.
Based on the Impanga conference on algebraic geometry
Bedlewo # july 4-10, 2010 Pragacz, Piotr | European Mathematical Society 2012 Nouveau

Arithmetical algebraic geometry
proceedings of a conference held at Purdue University
Dec. 5-7 Schilling, O. F. G. | Harper & Row, Publishers 1965 Nouveau

Algebriac geometry :
proceedings of the 3rd midwest conference on... held at the university of michigan#Nov. 14-15 Dolgachev, I. | Springer-Verlag 1983 Nouveau

Algebraic geometry in East Asia - Seoul 2008
Proceedings of the 3rd international conference
Seoul # november 11-15, 2008 Keum, JongHae ; Kondo, Shigeyuki ; Konno, Kazuhiro ; Oguiso, Keiji | Mathematical Society of Japan 2010 Nouveau

Actes du colloque de théorie de Hodge :
Luminy#Juin 1 - 6 | Société Mathématique de France 1989 Nouveau