# zbMATH — the first resource for mathematics

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 Documents Indexed: 46 Publications since 1997, including 7 Books
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#### Co-Authors

 22 single-authored 5 Prasad, Gopal 4 Conrad, Keith 2 Cais, Bryden 2 Diamond, Fred 2 Gabber, Ofer 2 Stein, William A. 2 Taylor, Richard Lawrence 1 Bertolini, Massimo 1 Breuil, Christophe 1 Brochard, Sylvain 1 Chai, Chingli 1 Darmon, Henri René 1 de Jong, Aise Johan 1 Edixhoven, Bas 1 Gross, Robert A. 1 Helfgott, Harald Andrés 1 Lieblich, Max David 1 Mitzenmacher, Michael 1 Oesterlé, Joseph 1 Olsson, Martin C. 1 Oort, Frans 1 Prasanna, Kartik 1 Rubin, Karl Cooper 1 Temkin, Michael 1 Wong, Siman 1 Yu, Jiu-Kang
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#### Serials

 6 Journal für die Reine und Angewandte Mathematik 3 Journal of the Ramanujan Mathematical Society 2 Annales de l’Institut Fourier 2 Compositio Mathematica 2 Journal of Number Theory 2 Journal of the American Mathematical Society 2 L’Enseignement Mathématique. 2e Série 2 Journal of Algebraic Geometry 2 Journal of the Institute of Mathematics of Jussieu 2 New Mathematical Monographs 1 IEEE Transactions on Information Theory 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Journal of Algebra 1 Michigan Mathematical Journal 1 Transactions of the American Mathematical Society 1 Mathematical Research Letters 1 Documenta Mathematica 1 Pure and Applied Mathematics Quarterly 1 Annals of Mathematics Studies 1 Lecture Notes in Mathematics 1 Mathematical Surveys and Monographs 1 IAS/Park City Mathematics Series 1 Panoramas et Synthèses
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#### Fields

 34 Algebraic geometry (14-XX) 22 Number theory (11-XX) 9 Group theory and generalizations (20-XX) 3 Commutative algebra (13-XX) 2 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Probability theory and stochastic processes (60-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

41 Publications have been cited 933 times in 807 Documents Cited by Year
On the modularity of elliptic curves over $$\mathbb Q$$: wild 3-adic exercises. Zbl 0982.11033
Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard
2001
Grothendieck duality and base change. Zbl 0992.14001
2000
Irreducible components of rigid spaces. Zbl 0928.32011
1999
Pseudo-reductive groups. Zbl 1216.20038
2010
Modularity of certain potentially Barsotti-Tate Galois representations. Zbl 0923.11085
Conrad, Brian; Diamond, Fred; Taylor, Richard
1999
Pseudo-reductive groups. 2nd ed. Zbl 1314.20037
2015
Deligne’s notes on Nagata compactifications. Zbl 1142.14001
2007
Reductive group schemes. Zbl 1349.14151
2014
A modern proof of Chevalley’s theorem on algebraic groups. Zbl 1007.14005
2002
Chow’s $$K/k$$-image and $$K/k$$-trace, and the Lang-Néron theorem. Zbl 1133.14028
2006
Arithmetic moduli of generalized elliptic curves. Zbl 1140.14018
2007
Nagata compactification for algebraic spaces. Zbl 1255.14003
Conrad, Brian; Lieblich, Max; Olsson, Martin
2012
Relative ampleness in rigid geometry. Zbl 1125.14009
2006
Complex multiplication and lifting problems. Zbl 1298.14001
Chai, Ching-Li; Conrad, Brian; Oort, Frans
2014
Gross-Zagier revisited (with an appendix by W. R. Mann). Zbl 1072.11040
2004
$$J_1(p)$$ has connected fibers. Zbl 1101.14311
Conrad, Brian; Edixhoven, Bas; Stein, William
2003
Finiteness theorems for algebraic groups over function fields. Zbl 1261.20049
2012
Finite group schemes over bases with low ramification. Zbl 0984.14015
1999
Weil and Grothendieck approaches to adelic points. Zbl 1316.14002
2012
On quasi-reductive group schemes. Zbl 1112.14053
2006
Several approaches to non-archimedean geometry. Zbl 1153.14020
2008
Approximation of versal deformations. Zbl 1087.14004
Conrad, Brian; de Jong, A. J.
2002
Non-archimedean analytification of algebraic spaces. Zbl 1177.14048
2009
Component groups of purely toric quotients. Zbl 1081.11040
2001
Prime specialization in genus 0. Zbl 1222.11113
2008
Modular curves and Ramanujan’s continued fraction. Zbl 1147.11032
2006
Root numbers and ranks in positive characteristic. Zbl 1113.11033
2005
$$p$$-adic $$L$$-functions and the coniveau filtration on Chow groups. With an appendix by Brian Conrad. Zbl 1436.11141
Bertolini, Massimo; Darmon, Henri; Prasanna, Kartik; Conrad, Brian
2017
Non-split reductive groups over $$\mathbb Z$$. Zbl 1356.14033
2015
Modular curves and rigid-analytic spaces. Zbl 1156.14312
2006
The flat deformation functor. Zbl 0927.11037
1997
Ramified deformation problems. Zbl 0997.11042
1999
The Möbius function and the residue theorem. Zbl 1148.11058
2005
Classification of pseudo-reductive groups. Zbl 1342.20048
2016
The structure of solvable groups over general fields. Zbl 1356.20026
2015
On group schemes. A celebration of SGA3. Lecture notes of the summer school “Group schemes, an introduction to the SGA3 seminar of Demazure-Grothendieck”, CIRM, Luminy, France, August 29 – September 9, 2011. Volume I. Zbl 1308.14047
Brochard, Sylvain; Conrad, Brian; Oesterlé, Joseph
2014
Power laws for monkeys typing randomly: the case of unequal probabilities. Zbl 1296.94053
2004
Arithmetic algebraic geometry. Expanded lectures delivered at the graduate summer school of the Institute for Advanced Study/Park City Mathematics Institute, Park City, UT, USA, June 20–July 10, 1999. Zbl 0974.00034
Conrad, Brian (ed.); Rubin, Karl (ed.)
2001
Inertia groups and fibers. Zbl 1018.14004
2000
Structure and classification of pseudo-reductive groups. Zbl 06863725
2017
Prime specialization in higher genus. I. Zbl 1158.11038
2008
$$p$$-adic $$L$$-functions and the coniveau filtration on Chow groups. With an appendix by Brian Conrad. Zbl 1436.11141
Bertolini, Massimo; Darmon, Henri; Prasanna, Kartik; Conrad, Brian
2017
Structure and classification of pseudo-reductive groups. Zbl 06863725
2017
Classification of pseudo-reductive groups. Zbl 1342.20048
2016
Pseudo-reductive groups. 2nd ed. Zbl 1314.20037
2015
Non-split reductive groups over $$\mathbb Z$$. Zbl 1356.14033
2015
The structure of solvable groups over general fields. Zbl 1356.20026
2015
Reductive group schemes. Zbl 1349.14151
2014
Complex multiplication and lifting problems. Zbl 1298.14001
Chai, Ching-Li; Conrad, Brian; Oort, Frans
2014
On group schemes. A celebration of SGA3. Lecture notes of the summer school “Group schemes, an introduction to the SGA3 seminar of Demazure-Grothendieck”, CIRM, Luminy, France, August 29 – September 9, 2011. Volume I. Zbl 1308.14047
Brochard, Sylvain; Conrad, Brian; Oesterlé, Joseph
2014
Nagata compactification for algebraic spaces. Zbl 1255.14003
Conrad, Brian; Lieblich, Max; Olsson, Martin
2012
Finiteness theorems for algebraic groups over function fields. Zbl 1261.20049
2012
Weil and Grothendieck approaches to adelic points. Zbl 1316.14002
2012
Pseudo-reductive groups. Zbl 1216.20038
2010
Non-archimedean analytification of algebraic spaces. Zbl 1177.14048
2009
Several approaches to non-archimedean geometry. Zbl 1153.14020
2008
Prime specialization in genus 0. Zbl 1222.11113
2008
Prime specialization in higher genus. I. Zbl 1158.11038
2008
Deligne’s notes on Nagata compactifications. Zbl 1142.14001
2007
Arithmetic moduli of generalized elliptic curves. Zbl 1140.14018
2007
Chow’s $$K/k$$-image and $$K/k$$-trace, and the Lang-Néron theorem. Zbl 1133.14028
2006
Relative ampleness in rigid geometry. Zbl 1125.14009
2006
On quasi-reductive group schemes. Zbl 1112.14053
2006
Modular curves and Ramanujan’s continued fraction. Zbl 1147.11032
2006
Modular curves and rigid-analytic spaces. Zbl 1156.14312
2006
Root numbers and ranks in positive characteristic. Zbl 1113.11033
2005
The Möbius function and the residue theorem. Zbl 1148.11058
2005
Gross-Zagier revisited (with an appendix by W. R. Mann). Zbl 1072.11040
2004
Power laws for monkeys typing randomly: the case of unequal probabilities. Zbl 1296.94053
2004
$$J_1(p)$$ has connected fibers. Zbl 1101.14311
Conrad, Brian; Edixhoven, Bas; Stein, William
2003
A modern proof of Chevalley’s theorem on algebraic groups. Zbl 1007.14005
2002
Approximation of versal deformations. Zbl 1087.14004
Conrad, Brian; de Jong, A. J.
2002
On the modularity of elliptic curves over $$\mathbb Q$$: wild 3-adic exercises. Zbl 0982.11033
Breuil, Christophe; Conrad, Brian; Diamond, Fred; Taylor, Richard
2001
Component groups of purely toric quotients. Zbl 1081.11040
2001
Arithmetic algebraic geometry. Expanded lectures delivered at the graduate summer school of the Institute for Advanced Study/Park City Mathematics Institute, Park City, UT, USA, June 20–July 10, 1999. Zbl 0974.00034
Conrad, Brian (ed.); Rubin, Karl (ed.)
2001
Grothendieck duality and base change. Zbl 0992.14001
2000
Inertia groups and fibers. Zbl 1018.14004
2000
Irreducible components of rigid spaces. Zbl 0928.32011
1999
Modularity of certain potentially Barsotti-Tate Galois representations. Zbl 0923.11085
Conrad, Brian; Diamond, Fred; Taylor, Richard
1999
Finite group schemes over bases with low ramification. Zbl 0984.14015
1999
Ramified deformation problems. Zbl 0997.11042
1999
The flat deformation functor. Zbl 0927.11037
1997
all top 5

#### Cited by 842 Authors

 11 Conrad, Brian 11 Gee, Toby 11 Temkin, Michael 10 Bennett, Michael A. 9 Bleher, Frauke M. 9 Schimmrigk, Rolf 9 Siksek, Samir 8 Gonzalez-Avilés, Cristian D. 7 Brion, Michel 7 Darmon, Henri René 7 Nicaise, Johannes 7 Stein, William A. 6 Bertolini, Massimo 6 Guitart, Xavier 6 Kisin, Mark 6 Papikian, Mihran 6 Park, Yoon Kyung 5 Česnavičius, Kęstutis 5 Delaunay, Christophe 5 Emerton, Matthew 5 Halle, Lars Halvard 5 Javanpeykar, Ariyan 5 Koch, Alan 5 McNinch, George J. 5 Newton, James 5 Nguyêñ Duy Tân 5 Poonen, Bjorn 5 Rabinoff, Joseph 5 Rydh, David 5 Savitt, David 4 Arteche, Giancarlo Lucchini 4 Bertapelle, Alessandra 4 Böckle, Gebhard 4 Byeon, Dongho 4 Calegari, Frank 4 Cao, Yang 4 Chinburg, Ted 4 Cho, Bumkyu 4 Conrad, Keith 4 Diamond, Fred 4 Geraghty, David 4 Gubler, Walter Bruno 4 Klosin, Krzysztof 4 Laurinčikas, Antanas 4 Le Hung, Bao V. 4 Levin, Brandon 4 Lorenzini, Dino J. 4 Mazur, Barry 4 Morra, Stefano 4 Murfet, Daniel 4 Murty, Maruti Ram 4 Nguyễn Quôc Thăng 4 Olsson, Martin C. 4 Pappas, Georgios 4 Prasanna, Kartik 4 Richarz, Timo 4 Silverberg, Alice 4 Taylor, Richard Lawrence 4 Ulmer, Douglas L. 4 Virdol, Cristian 4 Yu, Tony Yue 3 Alonso Tarrío, Leovigildo M. 3 Bary-Soroker, Lior 3 Bayer-Fluckiger, Eva 3 Bitan, Rony A. 3 Borovoi, Mikhail V. 3 Burungale, Ashay A. 3 Caruso, Xavier 3 Chen, Imin 3 Chenevier, Gaëtan 3 Creutz, Brendan 3 Dahmen, Sander R. 3 David, Chantal 3 Dieulefait, Luis Victor 3 Freitas, Nuno 3 Garibaldi, Skip 3 González-Jiménez, Enrique 3 Haines, Thomas J. 3 Hall, Jack 3 Harris, Michael Howard 3 Herzig, Florian 3 Ile, Runar 3 Jeremías López, Ana 3 Kapranov, Mikhail M. 3 Kedlaya, Kiran Sridhara 3 Kisilevsky, Hershy 3 Kovács, Sándor J. 3 Kumar, Narasimha 3 Le, Daniel 3 Lee, Yoonjin 3 Llosent, Giovanna 3 Loughran, Daniel 3 Masdeu, Marc 3 Meier, Lennart 3 Miller, Steven J. 3 Mitsui, Kentaro 3 Mohammadi, Amir 3 Pasten, Hector V. 3 Patakfalvi, Zsolt 3 Petersen, Sebastian ...and 742 more Authors
all top 5

#### Cited in 140 Serials

 72 Journal of Number Theory 36 Advances in Mathematics 36 Journal of Algebra 34 Compositio Mathematica 32 Duke Mathematical Journal 25 Mathematische Annalen 23 Annales de l’Institut Fourier 21 Journal of the American Mathematical Society 21 Journal of Algebraic Geometry 21 International Journal of Number Theory 20 Transactions of the American Mathematical Society 19 Inventiones Mathematicae 18 Journal de Théorie des Nombres de Bordeaux 17 Mathematische Zeitschrift 16 Mathematics of Computation 16 Journal für die Reine und Angewandte Mathematik 15 Journal of Pure and Applied Algebra 14 Journal of the Institute of Mathematics of Jussieu 12 Proceedings of the American Mathematical Society 12 Algebra & Number Theory 11 Israel Journal of Mathematics 11 Annals of Mathematics. Second Series 10 Communications in Algebra 10 Bulletin of the American Mathematical Society. New Series 10 Forum of Mathematics, Sigma 9 Transformation Groups 8 Functiones et Approximatio. Commentarii Mathematici 8 Manuscripta Mathematica 8 Documenta Mathematica 7 Memoirs of the American Mathematical Society 7 Experimental Mathematics 7 Selecta Mathematica. New Series 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Acta Arithmetica 6 Pacific Journal of Mathematics 6 The Ramanujan Journal 6 Research in the Mathematical Sciences 5 Archiv der Mathematik 5 Rendiconti del Seminario Matematico della Università di Padova 5 Research in Number Theory 4 Journal of Geometry and Physics 4 Journal of the London Mathematical Society. Second Series 4 Michigan Mathematical Journal 4 Journal of the European Mathematical Society (JEMS) 4 European Journal of Mathematics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Nuclear Physics. B 3 Publications Mathématiques 3 Journal of the Mathematical Society of Japan 3 Nagoya Mathematical Journal 3 Expositiones Mathematicae 3 Algebras and Representation Theory 3 Science China. Mathematics 3 Journal de l’École Polytechnique – Mathématiques 2 International Journal of Modern Physics A 2 American Mathematical Monthly 2 Mathematical Notes 2 Russian Mathematical Surveys 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Geometriae Dedicata 2 Proceedings of the London Mathematical Society. Third Series 2 Tohoku Mathematical Journal. Second Series 2 Tokyo Journal of Mathematics 2 International Journal of Mathematics 2 Geometric and Functional Analysis. GAFA 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 St. Petersburg Mathematical Journal 2 Journal of Lie Theory 2 Algebraic & Geometric Topology 2 Kyoto Journal of Mathematics 2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 2 Forum of Mathematics, Pi 1 Modern Physics Letters A 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Journal d’Analyse Mathématique 1 Lithuanian Mathematical Journal 1 Rocky Mountain Journal of Mathematics 1 Acta Mathematica 1 Acta Mathematica Vietnamica 1 Bulletin of the London Mathematical Society 1 Canadian Journal of Mathematics 1 Dissertationes Mathematicae 1 Glasgow Mathematical Journal 1 Indiana University Mathematics Journal 1 International Journal of Mathematics and Mathematical Sciences 1 Journal of Approximation Theory 1 Journal of Computational and Applied Mathematics 1 Le Matematiche 1 Mathematische Nachrichten 1 Mathematika 1 Monatshefte für Mathematik 1 Osaka Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the Japan Academy. Series A 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 Revista de la Unión Matemática Argentina ...and 40 more Serials
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#### Cited in 35 Fields

 485 Number theory (11-XX) 462 Algebraic geometry (14-XX) 85 Group theory and generalizations (20-XX) 45 Category theory; homological algebra (18-XX) 39 Commutative algebra (13-XX) 34 Topological groups, Lie groups (22-XX) 30 Several complex variables and analytic spaces (32-XX) 26 Associative rings and algebras (16-XX) 17 Field theory and polynomials (12-XX) 12 Algebraic topology (55-XX) 10 $$K$$-theory (19-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Differential geometry (53-XX) 8 Nonassociative rings and algebras (17-XX) 8 Quantum theory (81-XX) 7 Mathematical logic and foundations (03-XX) 6 Relativity and gravitational theory (83-XX) 5 Information and communication theory, circuits (94-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Geometry (51-XX) 4 Manifolds and cell complexes (57-XX) 4 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 3 Measure and integration (28-XX) 3 Special functions (33-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Functional analysis (46-XX) 2 General topology (54-XX) 2 Computer science (68-XX) 2 Mathematics education (97-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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