Edit Profile (opens in new tab) Schoutens, Hans Co-Author Distance Author ID: schoutens.hans Published as: Schoutens, Hans; Schoutens, H. Videos: carmin.tv Documents Indexed: 55 Publications since 1988, including 1 Book and 8 Additional arXiv Preprints Reviewing Activity: 7 Reviews Co-Authors: 12 Co-Authors with 10 Joint Publications 368 Co-Co-Authors all top 5 Co-Authors 45 single-authored 3 Gardener, T. S. 3 Miller, Russell G. 1 Aschenbrenner, Matthias 1 Denef, Jan 1 Heinzer, William J. 1 Kalimullin, Iskander Shagitovich 1 Li, Charles Chun Che 1 Loper, Kenneth Alan 1 Olberding, Bruce M. 1 Poonen, Bjorn 1 Shlapentokh, Alexandra 1 Toeniskoetter, Matthew all top 5 Serials 7 Journal of Algebra 3 Communications in Algebra 3 The Journal of Symbolic Logic 2 Israel Journal of Mathematics 2 Compositio Mathematica 2 Pacific Journal of Mathematics 2 Proceedings of the American Mathematical Society 2 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Rocky Mountain Journal of Mathematics 1 Beiträge zur Algebra und Geometrie 1 Illinois Journal of Mathematics 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Monatshefte für Mathematik 1 Proceedings of the London Mathematical Society. Third Series 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 Transactions of the American Mathematical Society 1 Annals of Pure and Applied Logic 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Journal of Algebraic Geometry 1 Annales Mathematicae Silesianae 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 JP Journal of Algebra, Number Theory and Applications 1 Journal of Algebra and its Applications 1 Lecture Notes in Mathematics 1 Computability all top 5 Fields 37 Commutative algebra (13-XX) 17 Algebraic geometry (14-XX) 16 Mathematical logic and foundations (03-XX) 9 Several complex variables and analytic spaces (32-XX) 7 Field theory and polynomials (12-XX) 4 Category theory; homological algebra (18-XX) 1 General algebraic systems (08-XX) 1 \(K\)-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 42 Publications have been cited 302 times in 187 Documents Cited by ▼ Year ▼ A computable functor from graphs to fields. Zbl 1447.03005 Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 40 2018 The use of ultraproducts in commutative algebra. Zbl 1205.13002 Schoutens, Hans 37 2010 Projective dimension and the singular locus. Zbl 1014.13003 Schoutens, Hans 16 2003 Non-standard tight closure for affine \(\mathbb C\)-algebras. Zbl 1082.13005 Schoutens, Hans 13 2003 Ideal theory of infinite directed unions of local quadratic transforms. Zbl 1365.13036 Heinzer, William; Loper, K. Alan; Olberding, Bruce; Schoutens, Hans; Toeniskoetter, Matthew 13 2017 Rigid subanalytic sets. Zbl 0867.32012 Schoutens, Hans 11 1994 Canonical big Cohen-Macaulay algebras and rational singularities. Zbl 1045.13005 Schoutens, Hans 10 2004 Log-terminal singularities and vanishing theorems via non-standard tight closure. Zbl 1070.14005 Schoutens, Hans 10 2005 Computably categorical fields via Fermat’s last theorem. Zbl 1408.03029 Miller, Russell; Schoutens, Hans 10 2013 Existentially closed models of the theory of Artinian local rings. Zbl 1060.03056 Schoutens, Hans 9 1999 Bounds in cohomology. Zbl 0953.13005 Schoutens, Hans 9 2000 Lefschetz extensions, tight closure and big Cohen-Macaulay algebras. Zbl 1156.13011 Aschenbrenner, Matthias; Schoutens, Hans 8 2007 Mixed characteristic homological theorems in low degrees. Zbl 1049.13009 Schoutens, Hans 7 2003 On the vanishing of Tor of the absolute integral closure. Zbl 1050.13004 Schoutens, Hans 7 2004 O-minimalism. Zbl 1337.03055 Schoutens, Hans 7 2014 On the decidability of the existential theory of \(\mathbb{F}_p[[t]]\). Zbl 1046.12006 Denef, Jan; Schoutens, Hans 6 2003 A non-standard proof of the Briançon-Skoda theorem. Zbl 1005.13007 Schoutens, Hans 6 2003 Lefschetz principle applied to symbolic powers. Zbl 1095.13031 Schoutens, Hans 6 2003 Approximation properties for some non-Noetherian local rings. Zbl 0608.13008 Schoutens, H. 6 1988 Uniformization of rigid subanalytic sets. Zbl 0867.32011 Schoutens, Hans 6 1994 Pure subrings of regular rings are pseudo-rational. Zbl 1133.14002 Schoutens, Hans 6 2008 Uniform bounds in algebraic geometry and commutative algebra. Zbl 1092.13513 Schoutens, Hans 6 2000 Rigid subanalytic sets in the plane. Zbl 0826.14014 Schoutens, Hans 6 1994 Classifying singularities up to analytic extensions of scalars is smooth. Zbl 1228.14007 Schoutens, Hans 5 2011 Embedded resolution of singularities in rigid analytic geometry. Zbl 0972.32018 Schoutens, Hans 4 1999 Asymptotic homological conjectures in mixed characteristic. Zbl 1147.13006 Schoutens, Hans 4 2007 Hochster’s small MCM conjecture for three-dimensional weakly F-split rings. Zbl 1453.13048 Schoutens, Hans 4 2017 Closure of rigid semianalytic sets. Zbl 0949.14034 Schoutens, Hans 3 1997 Blowing up in rigid analytic geometry. Zbl 0854.32020 Schoutens, Hans 3 1995 Flattening and subanalytic sets in rigid analytic geometry. Zbl 1047.32016 Gardener, T. S.; Schoutens, Hans 3 2001 Characteristic \(p\) methods in characteristic zero via ultraproducts. Zbl 1276.13007 Schoutens, Hans 3 2011 Number of generators of a Cohen-Macaulay ideal. Zbl 1107.13022 Schoutens, Hans 2 2003 Artin approximation via the model theory of Cohen-Macaulay rings. Zbl 0947.03052 Schoutens, Hans 2 2000 A differential-algebraic criterion for obtaining a small Cohen-Macaulay module. Zbl 1440.13068 Schoutens, Hans 2 2020 Absolute bounds on the number of generators of Cohen-Macaulay ideals of height two. Zbl 1126.13016 Schoutens, Hans 2 2006 Dimension and singularity theory for local rings of finite embedding dimension. Zbl 1320.13031 Schoutens, Hans 2 2013 Constructible invariants. Zbl 1111.13019 Schoutens, Hans 2 2006 Degree spectra for transcendence in fields. Zbl 1434.03096 Kalimullin, Iskander; Miller, Russell; Schoutens, Hans 2 2019 Rigid analytic flatificators. Zbl 0953.32017 Schoutens, Hans 1 1999 A local flatness criterion for complete modules. Zbl 1115.13017 Schoutens, Hans 1 2007 The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron. Zbl 1386.14090 Schoutens, Hans 1 2016 The theory of ordinal length. Zbl 1335.13015 Schoutens, Hans 1 2016 A differential-algebraic criterion for obtaining a small Cohen-Macaulay module. Zbl 1440.13068 Schoutens, Hans 2 2020 Degree spectra for transcendence in fields. Zbl 1434.03096 Kalimullin, Iskander; Miller, Russell; Schoutens, Hans 2 2019 A computable functor from graphs to fields. Zbl 1447.03005 Miller, Russell; Poonen, Bjorn; Schoutens, Hans; Shlapentokh, Alexandra 40 2018 Ideal theory of infinite directed unions of local quadratic transforms. Zbl 1365.13036 Heinzer, William; Loper, K. Alan; Olberding, Bruce; Schoutens, Hans; Toeniskoetter, Matthew 13 2017 Hochster’s small MCM conjecture for three-dimensional weakly F-split rings. Zbl 1453.13048 Schoutens, Hans 4 2017 The motivic Igusa zeta series of some hypersurfaces non-degenerated with respect to their Newton polyhedron. Zbl 1386.14090 Schoutens, Hans 1 2016 The theory of ordinal length. Zbl 1335.13015 Schoutens, Hans 1 2016 O-minimalism. Zbl 1337.03055 Schoutens, Hans 7 2014 Computably categorical fields via Fermat’s last theorem. Zbl 1408.03029 Miller, Russell; Schoutens, Hans 10 2013 Dimension and singularity theory for local rings of finite embedding dimension. Zbl 1320.13031 Schoutens, Hans 2 2013 Classifying singularities up to analytic extensions of scalars is smooth. Zbl 1228.14007 Schoutens, Hans 5 2011 Characteristic \(p\) methods in characteristic zero via ultraproducts. Zbl 1276.13007 Schoutens, Hans 3 2011 The use of ultraproducts in commutative algebra. Zbl 1205.13002 Schoutens, Hans 37 2010 Pure subrings of regular rings are pseudo-rational. Zbl 1133.14002 Schoutens, Hans 6 2008 Lefschetz extensions, tight closure and big Cohen-Macaulay algebras. Zbl 1156.13011 Aschenbrenner, Matthias; Schoutens, Hans 8 2007 Asymptotic homological conjectures in mixed characteristic. Zbl 1147.13006 Schoutens, Hans 4 2007 A local flatness criterion for complete modules. Zbl 1115.13017 Schoutens, Hans 1 2007 Absolute bounds on the number of generators of Cohen-Macaulay ideals of height two. Zbl 1126.13016 Schoutens, Hans 2 2006 Constructible invariants. Zbl 1111.13019 Schoutens, Hans 2 2006 Log-terminal singularities and vanishing theorems via non-standard tight closure. Zbl 1070.14005 Schoutens, Hans 10 2005 Canonical big Cohen-Macaulay algebras and rational singularities. Zbl 1045.13005 Schoutens, Hans 10 2004 On the vanishing of Tor of the absolute integral closure. Zbl 1050.13004 Schoutens, Hans 7 2004 Projective dimension and the singular locus. Zbl 1014.13003 Schoutens, Hans 16 2003 Non-standard tight closure for affine \(\mathbb C\)-algebras. Zbl 1082.13005 Schoutens, Hans 13 2003 Mixed characteristic homological theorems in low degrees. Zbl 1049.13009 Schoutens, Hans 7 2003 On the decidability of the existential theory of \(\mathbb{F}_p[[t]]\). Zbl 1046.12006 Denef, Jan; Schoutens, Hans 6 2003 A non-standard proof of the Briançon-Skoda theorem. Zbl 1005.13007 Schoutens, Hans 6 2003 Lefschetz principle applied to symbolic powers. Zbl 1095.13031 Schoutens, Hans 6 2003 Number of generators of a Cohen-Macaulay ideal. Zbl 1107.13022 Schoutens, Hans 2 2003 Flattening and subanalytic sets in rigid analytic geometry. Zbl 1047.32016 Gardener, T. S.; Schoutens, Hans 3 2001 Bounds in cohomology. Zbl 0953.13005 Schoutens, Hans 9 2000 Uniform bounds in algebraic geometry and commutative algebra. Zbl 1092.13513 Schoutens, Hans 6 2000 Artin approximation via the model theory of Cohen-Macaulay rings. Zbl 0947.03052 Schoutens, Hans 2 2000 Existentially closed models of the theory of Artinian local rings. Zbl 1060.03056 Schoutens, Hans 9 1999 Embedded resolution of singularities in rigid analytic geometry. Zbl 0972.32018 Schoutens, Hans 4 1999 Rigid analytic flatificators. Zbl 0953.32017 Schoutens, Hans 1 1999 Closure of rigid semianalytic sets. Zbl 0949.14034 Schoutens, Hans 3 1997 Blowing up in rigid analytic geometry. Zbl 0854.32020 Schoutens, Hans 3 1995 Rigid subanalytic sets. Zbl 0867.32012 Schoutens, Hans 11 1994 Uniformization of rigid subanalytic sets. Zbl 0867.32011 Schoutens, Hans 6 1994 Rigid subanalytic sets in the plane. Zbl 0826.14014 Schoutens, Hans 6 1994 Approximation properties for some non-Noetherian local rings. Zbl 0608.13008 Schoutens, H. 6 1988 all cited Publications top 5 cited Publications all top 5 Cited by 219 Authors 24 Schoutens, Hans 12 Miller, Russell G. 10 Bazhenov, Nikolaĭ Alekseevich 8 Olberding, Bruce M. 6 Harrison-Trainor, Matthew 6 Melnikov, Alexander G. 5 Kalimullin, Iskander Shagitovich 5 Knight, Julia F. 4 Heinzer, William J. 4 Kogabaev, Nurlan Talgatovich 4 Loper, Kenneth Alan 4 Toeniskoetter, Matthew 4 Vatev, Stefan V. 3 Downey, Rodney Graham 3 Guerrieri, Lorenzo 3 Iyengar, Srikanth B. 3 Montalbán, Antonio 3 Ng, KengMeng 3 Rossegger, Dino 3 Shlapentokh, Alexandra 3 Takahashi, Ryo 3 Turetsky, Daniel D. 2 Alvir, Rachael 2 Erman, Daniel 2 Finocchiaro, Carmelo Antonio 2 Frolov, Andreĭ Nikolaevich 2 Fujita, Masato 2 Gallego, Edisson 2 Ganchev, Hristo A. 2 Gómez-Ramírez, Danny Arlen de Jesús 2 Granja, Angel 2 Grover, Vinod K. 2 Harman, Nate 2 Hirschfeldt, Denis Roman 2 Kalinov, Daniil 2 Lipshitz, Leonard 2 Martin, Florent 2 R. G., Rebecca 2 Sam, Steven V. 2 Sankaran, N. 2 Sato, Kenta 2 Snowden, Andrew W. 2 Soskova, Alexandra A. 2 Spirito, Dario 2 Stout, Andrew R. 2 Tavanfar, Ehsan 2 Vélez, Juan Diego 2 Yamaguchi, Tatsuki 1 Alaev, Pavel Evgenievich 1 Albrecher, Hansjörg 1 Andersen, Henning Haahr 1 André, Yves 1 Andruszkiewicz, Ryszard Romuald 1 Anscombe, Sylvy 1 Arapura, Donu 1 Ardakov, Konstantin 1 Aschenbrenner, Matthias 1 Ballard, Matthew Robert 1 Barthel, Tobias 1 Bélair, Luc 1 Belitskii, Genrich R. 1 Bell, Jason P. 1 Benaim, Shalom 1 Bleybel, Ali 1 Bode, Andreas 1 Boix, Alberto Fernandez 1 Bouchiba, Samir 1 Boulier, François 1 Braun, Lukas 1 Brenner, Holger 1 Bridgeland, Tom 1 Brünjes, Lars 1 Burchfield, Hannah 1 Calvert, Wesley 1 Cani, Arian 1 Carocci, Francesca 1 Casalaina-Martin, Sebastian 1 Çelikler, Y. Firat 1 Chubb, Jennifer 1 Cluckers, Raf 1 Conca, Aldo 1 Conrad, Brian 1 Corniani, Elsa 1 Csima, Barbara F. 1 Cubides Kovacsics, Pablo 1 Cutkosky, Steven Dale 1 Dietz, Geoffrey D. 1 Dittmann, Philip 1 Ducros, Antoine 1 Dyckerhoff, Tobias 1 Etingof, Pavel Il’ich 1 Faber, Eleonore 1 Falkensteiner, Sebastian 1 Favero, David 1 Fehm, Arno 1 Ferguson, Thomas Macaulay 1 Fernández Bretón, David José 1 Fiorot, Luisa 1 Flake, Johannes 1 Fontana, Marco ...and 119 more Authors all top 5 Cited in 75 Serials 16 Journal of Algebra 12 The Journal of Symbolic Logic 9 Algebra and Logic 7 Compositio Mathematica 6 Journal of Pure and Applied Algebra 6 Proceedings of the American Mathematical Society 5 Advances in Mathematics 5 Inventiones Mathematicae 5 Transactions of the American Mathematical Society 5 Annals of Pure and Applied Logic 5 Mathematical Logic Quarterly (MLQ) 4 Communications in Algebra 3 Manuscripta Mathematica 3 Nagoya Mathematical Journal 3 Archive for Mathematical Logic 3 Journal of Mathematical Sciences (New York) 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 Algebra & Number Theory 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Beiträge zur Algebra und Geometrie 2 Pacific Journal of Mathematics 2 Rendiconti del Seminario Matematico della Università di Padova 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Mathematical Finance 2 Journal of the European Mathematical Society (JEMS) 2 Journal of Mathematical Logic 2 Journal of Algebra and its Applications 2 Sibirskie Èlektronnye Matematicheskie Izvestiya 2 Journal of Commutative Algebra 1 American Mathematical Monthly 1 Israel Journal of Mathematics 1 Mathematische Semesterberichte 1 Periodica Mathematica Hungarica 1 Rocky Mountain Journal of Mathematics 1 Annales de l’Institut Fourier 1 Archiv der Mathematik 1 Duke Mathematical Journal 1 Fundamenta Mathematicae 1 Illinois Journal of Mathematics 1 Journal of Computer and System Sciences 1 Journal of Number Theory 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Memoirs of the American Mathematical Society 1 Monatshefte für Mathematik 1 Notre Dame Journal of Formal Logic 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the London Mathematical Society. Third Series 1 Results in Mathematics 1 Siberian Mathematical Journal 1 Studia Logica 1 Theoretical Computer Science 1 Bulletin of the Korean Mathematical Society 1 Journal of the American Mathematical Society 1 Publicacions Matemàtiques 1 International Journal of Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Journal of Logic, Language and Information 1 Journal of Algebraic Geometry 1 Bulletin of the Belgian Mathematical Society - Simon Stevin 1 Transformation Groups 1 Algebras and Representation Theory 1 Communications of the Korean Mathematical Society 1 Communications in Contemporary Mathematics 1 Lobachevskii Journal of Mathematics 1 Annales Mathematicae Silesianae 1 Quantitative Finance 1 Journal of the Australian Mathematical Society 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oberwolfach Reports 1 Logic and Analysis 1 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 1 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 1 Transactions of the American Mathematical Society. Series B all top 5 Cited in 28 Fields 76 Commutative algebra (13-XX) 73 Mathematical logic and foundations (03-XX) 58 Algebraic geometry (14-XX) 18 Field theory and polynomials (12-XX) 12 Several complex variables and analytic spaces (32-XX) 10 Category theory; homological algebra (18-XX) 9 Number theory (11-XX) 7 Associative rings and algebras (16-XX) 7 Group theory and generalizations (20-XX) 6 Order, lattices, ordered algebraic structures (06-XX) 5 Computer science (68-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Nonassociative rings and algebras (17-XX) 4 General topology (54-XX) 3 Geometry (51-XX) 3 Probability theory and stochastic processes (60-XX) 2 Combinatorics (05-XX) 2 Real functions (26-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 General algebraic systems (08-XX) 1 \(K\)-theory (19-XX) 1 Functions of a complex variable (30-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Algebraic topology (55-XX) Citations by Year