Edit Profile (opens in new tab) Asok, Aravind Co-Author Distance Author ID: asok.aravind Published as: Asok, Aravind; Asok, A. Homepage: https://dornsife.usc.edu/aravind-asok/ External Links: MGP · ORCID · arXiv · Google Scholar · ResearchGate Documents Indexed: 43 Publications since 2006, including 5 Additional arXiv Preprints Co-Authors: 17 Co-Authors with 34 Joint Publications 300 Co-Co-Authors all top 5 Co-Authors 9 single-authored 15 Fasel, Jean 5 Doran, Brent 5 Hopkins, Michael Jerome 5 Wendt, Matthias 4 Hoyois, Marc 2 Bachmann, Tom 2 Hasemeyer, Christian 2 Østvær, Paul Arne 2 Williams, Ben 1 Das, Mrinal Kanti 1 Déglise, Frédéric 1 Dubouloz, Adrien 1 Kebekus, Stefan 1 Kirwan, Frances Clare 1 Morel, Fabien 1 Nagel, Jan 1 Parson, James A. 1 Wickelgren, Kirsten G. all top 5 Serials 3 Duke Mathematical Journal 3 Journal of Topology 2 Advances in Mathematics 2 Compositio Mathematica 2 Journal of Pure and Applied Algebra 2 IMRN. International Mathematics Research Notices 2 Geometry & Topology 1 Bulletin of the London Mathematical Society 1 Inventiones Mathematicae 1 Journal of Algebra 1 Journal für die Reine und Angewandte Mathematik 1 Journal of the American Mathematical Society 1 Journal of the Ramanujan Mathematical Society 1 Bulletin of the American Mathematical Society. New Series 1 Mathematical Research Letters 1 Documenta Mathematica 1 Journal of the European Mathematical Society (JEMS) 1 Homology, Homotopy and Applications 1 The Quarterly Journal of Mathematics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 IMRP. International Mathematics Research Papers 1 Pure and Applied Mathematics Quarterly 1 Algebra & Number Theory 1 Electronic Research Announcements in Mathematical Sciences 1 Forum of Mathematics, Sigma 1 Algebraic Geometry all top 5 Fields 41 Algebraic geometry (14-XX) 24 Algebraic topology (55-XX) 18 \(K\)-theory (19-XX) 9 Commutative algebra (13-XX) 5 Group theory and generalizations (20-XX) 4 Category theory; homological algebra (18-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 34 Publications have been cited 341 times in 151 Documents Cited by ▼ Year ▼ Affine representability results in \(\mathbb{A}^1\)-homotopy theory. I: Vector bundles. Zbl 1401.14118 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 33 2017 Splitting vector bundles outside the stable range and \(\mathbb A^1\) – homotopy sheaves of punctured affine spaces. Zbl 1329.14045 Asok, Aravind; Fasel, Jean 29 2015 Affine representability results in \(\mathbb A^1\)-homotopy theory. II: Principal bundles and homogeneous spaces. Zbl 1400.14061 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 27 2018 Smooth varieties up to \(\mathbb A^1\)-homotopy and algebraic \(h\)-cobordisms. Zbl 1255.14018 Asok, Aravind; Morel, Fabien 26 2011 Algebraic vector bundles on spheres. Zbl 1326.14098 Asok, Aravind; Fasel, Jean 25 2014 A cohomological classification of vector bundles on smooth affine threefolds. Zbl 1314.14044 Asok, Aravind; Fasel, Jean 24 2014 Comparing Euler classes. Zbl 1372.14013 Asok, A.; Fasel, J. 24 2016 An explicit \(KO\)-degree map and applications. Zbl 1400.14060 Asok, Aravind; Fasel, Jean 19 2017 Secondary characteristic classes and the Euler class. Zbl 1349.14078 Asok, Aravind; Fasel, Jean 16 2015 Smooth models of motivic spheres and the clutching construction. Zbl 1405.14050 Asok, Aravind; Doran, Brent; Fasel, Jean 14 2017 The simplicial suspension sequence in \(\mathbb A^1\)-homotopy. Zbl 1365.14027 Asok, Aravind; Wickelgren, Kirsten; Williams, Ben 11 2017 On unipotent quotients and some \(\mathbb A^1\)-contractible smooth schemes. Zbl 1157.14032 Asok, Aravind; Doran, Brent 11 2007 Birational invariants and \(\mathbb{A}^1\)-connectedness. Zbl 1328.14036 Asok, Aravind 10 2013 Affine representability results in \(\mathbb A^1\)-homotopy theory. III: Finite fields and complements. Zbl 1505.14050 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 9 2020 Rationality problems and conjectures of Milnor and Bloch-Kato. Zbl 1279.14063 Asok, Aravind 8 2013 Stable \(\mathbb A^1\)-homotopy and \(R\)-equivalence. Zbl 1244.14016 Asok, Aravind; Haesemeyer, Christian 7 2011 \(\mathbb A^1\)-homotopy groups, excision, and solvable quotients. Zbl 1190.14018 Asok, Aravind; Doran, Brent 6 2009 Vector bundles on contractible smooth schemes. Zbl 1167.14025 Asok, Aravind; Doran, Brent 5 2008 Motivic spheres and the image of the Suslin-Hurewicz map. Zbl 1444.19004 Asok, Aravind; Fasel, Jean; Williams, Ben 5 2020 Yang-Mills theory and Tamagawa numbers: The fascination of unexpected links in mathematics. Zbl 1166.14024 Asok, Aravind; Doran, Brent; Kirwan, Frances 4 2008 Euler class groups and motivic stable cohomotopy (with an appendix by Mrinal Kanti Das). Zbl 1487.14053 Asok, Aravind; Fasel, Jean 4 2022 Splitting vector bundles and \(\mathbb A^{1}\)-fundamental groups of higher-dimensional varieties. Zbl 1300.14024 Asok, Aravind 4 2013 Generically split octonion algebras and \(\mathbb{A}^1\)-homotopy theory. Zbl 1430.14051 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 4 2019 Obstructions to algebraizing topological vector bundles. Zbl 1504.14043 Asok, A.; Fasel, J.; Hopkins, M. J. 4 2019 Motives of some acyclic varieties. Zbl 1244.14015 Asok, Aravind 3 2011 About the cover: the mathematical imagery of Lun-Yi Tsai. Zbl 1197.00038 Asok, Aravind 1 2010 Stably \(\mathbb{A}^1\)-connected varieties and universal \(\mathrm{CH}_{0}\). Zbl 1423.14148 Asok, Aravind 1 2017 Comparing \(\mathbb{A}^1\)-\(h\)-cobordism and \(\mathbb{A}^1\)-weak equivalence. Zbl 1401.14058 Asok, Aravind; Kebekus, Stefan; Wendt, Matthias 1 2017 Equivariant vector bundles on certain affine \(G\)-varieties. Zbl 1110.14042 Asok, Aravind 1 2006 Affine representability of quadrics revisited. Zbl 1495.14034 Asok, Aravind 1 2022 Localization and nilpotent spaces in \(\mathbb{A}^1\)-homotopy theory. Zbl 1495.14035 Asok, Aravind; Fasel, Jean; Hopkins, Michael J. 1 2022 Vector bundles on algebraic varieties. Zbl 07823056 Asok, Aravind; Fasel, Jean 1 2023 The homotopy Leray spectral sequence. Zbl 1440.14122 Asok, Aravind; Déglise, Frédéric; Nagel, Jan 1 2020 \(\mathbb{A}^1\)-homotopy theory and contractible varieties: a survey. Zbl 1478.14001 Asok, Aravind; Østvær, Paul Arne 1 2021 Vector bundles on algebraic varieties. Zbl 07823056 Asok, Aravind; Fasel, Jean 1 2023 Euler class groups and motivic stable cohomotopy (with an appendix by Mrinal Kanti Das). Zbl 1487.14053 Asok, Aravind; Fasel, Jean 4 2022 Affine representability of quadrics revisited. Zbl 1495.14034 Asok, Aravind 1 2022 Localization and nilpotent spaces in \(\mathbb{A}^1\)-homotopy theory. Zbl 1495.14035 Asok, Aravind; Fasel, Jean; Hopkins, Michael J. 1 2022 \(\mathbb{A}^1\)-homotopy theory and contractible varieties: a survey. Zbl 1478.14001 Asok, Aravind; Østvær, Paul Arne 1 2021 Affine representability results in \(\mathbb A^1\)-homotopy theory. III: Finite fields and complements. Zbl 1505.14050 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 9 2020 Motivic spheres and the image of the Suslin-Hurewicz map. Zbl 1444.19004 Asok, Aravind; Fasel, Jean; Williams, Ben 5 2020 The homotopy Leray spectral sequence. Zbl 1440.14122 Asok, Aravind; Déglise, Frédéric; Nagel, Jan 1 2020 Generically split octonion algebras and \(\mathbb{A}^1\)-homotopy theory. Zbl 1430.14051 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 4 2019 Obstructions to algebraizing topological vector bundles. Zbl 1504.14043 Asok, A.; Fasel, J.; Hopkins, M. J. 4 2019 Affine representability results in \(\mathbb A^1\)-homotopy theory. II: Principal bundles and homogeneous spaces. Zbl 1400.14061 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 27 2018 Affine representability results in \(\mathbb{A}^1\)-homotopy theory. I: Vector bundles. Zbl 1401.14118 Asok, Aravind; Hoyois, Marc; Wendt, Matthias 33 2017 An explicit \(KO\)-degree map and applications. Zbl 1400.14060 Asok, Aravind; Fasel, Jean 19 2017 Smooth models of motivic spheres and the clutching construction. Zbl 1405.14050 Asok, Aravind; Doran, Brent; Fasel, Jean 14 2017 The simplicial suspension sequence in \(\mathbb A^1\)-homotopy. Zbl 1365.14027 Asok, Aravind; Wickelgren, Kirsten; Williams, Ben 11 2017 Stably \(\mathbb{A}^1\)-connected varieties and universal \(\mathrm{CH}_{0}\). Zbl 1423.14148 Asok, Aravind 1 2017 Comparing \(\mathbb{A}^1\)-\(h\)-cobordism and \(\mathbb{A}^1\)-weak equivalence. Zbl 1401.14058 Asok, Aravind; Kebekus, Stefan; Wendt, Matthias 1 2017 Comparing Euler classes. Zbl 1372.14013 Asok, A.; Fasel, J. 24 2016 Splitting vector bundles outside the stable range and \(\mathbb A^1\) – homotopy sheaves of punctured affine spaces. Zbl 1329.14045 Asok, Aravind; Fasel, Jean 29 2015 Secondary characteristic classes and the Euler class. Zbl 1349.14078 Asok, Aravind; Fasel, Jean 16 2015 Algebraic vector bundles on spheres. Zbl 1326.14098 Asok, Aravind; Fasel, Jean 25 2014 A cohomological classification of vector bundles on smooth affine threefolds. Zbl 1314.14044 Asok, Aravind; Fasel, Jean 24 2014 Birational invariants and \(\mathbb{A}^1\)-connectedness. Zbl 1328.14036 Asok, Aravind 10 2013 Rationality problems and conjectures of Milnor and Bloch-Kato. Zbl 1279.14063 Asok, Aravind 8 2013 Splitting vector bundles and \(\mathbb A^{1}\)-fundamental groups of higher-dimensional varieties. Zbl 1300.14024 Asok, Aravind 4 2013 Smooth varieties up to \(\mathbb A^1\)-homotopy and algebraic \(h\)-cobordisms. Zbl 1255.14018 Asok, Aravind; Morel, Fabien 26 2011 Stable \(\mathbb A^1\)-homotopy and \(R\)-equivalence. Zbl 1244.14016 Asok, Aravind; Haesemeyer, Christian 7 2011 Motives of some acyclic varieties. Zbl 1244.14015 Asok, Aravind 3 2011 About the cover: the mathematical imagery of Lun-Yi Tsai. Zbl 1197.00038 Asok, Aravind 1 2010 \(\mathbb A^1\)-homotopy groups, excision, and solvable quotients. Zbl 1190.14018 Asok, Aravind; Doran, Brent 6 2009 Vector bundles on contractible smooth schemes. Zbl 1167.14025 Asok, Aravind; Doran, Brent 5 2008 Yang-Mills theory and Tamagawa numbers: The fascination of unexpected links in mathematics. Zbl 1166.14024 Asok, Aravind; Doran, Brent; Kirwan, Frances 4 2008 On unipotent quotients and some \(\mathbb A^1\)-contractible smooth schemes. Zbl 1157.14032 Asok, Aravind; Doran, Brent 11 2007 Equivariant vector bundles on certain affine \(G\)-varieties. Zbl 1110.14042 Asok, Aravind 1 2006 all cited Publications top 5 cited Publications all top 5 Cited by 144 Authors 21 Asok, Aravind 12 Fasel, Jean 10 Wendt, Matthias 9 Østvær, Paul Arne 8 Wickelgren, Kirsten G. 7 Sawant, Anand 6 Balwe, Chetan T. 5 Bachmann, Tom 5 Schlichting, Marco 4 Hogadi, Amit 4 Hoyois, Marc 4 Levine, Marc Noel 4 Röndigs, Oliver 4 Syed, Tariq 4 Williams, Ben 3 Das, Mrinal Kanti 3 Hornbostel, Jens 3 Hoshi, Akinari 3 Rao, Ravi A. 3 Schreieder, Stefan 3 Stavrova, Anastasia K. 2 Bondarko, Mikhail Vladimirovich 2 Česnavičius, Kęstutis 2 Chintala, Vineeth Reddy 2 Choudhury, Utsav 2 Đào Phương Bắc 2 Déglise, Frédéric 2 Doran, Brent 2 Elmanto, Elden 2 Hopkins, Michael Jerome 2 Hutchinson, Kevin 2 Jose, Selby 2 Kang, Ming-Chang 2 Kass, Jesse Leo 2 Kelly, Shane P. 2 Khan, Adeel A. 2 Mandal, Satya 2 Mathew, Akhil 2 Mishra, Bibekananda 2 Morel, Fabien 2 Nguyễn Quôc Thăng 2 Ormsby, Kyle M. 2 Pauli, Sabrina 2 Petersson, Holger P. 2 Spitzweck, Markus 2 Tamme, Georg 2 Tikader, Soumi 2 Yakerson, Maria 2 Zibrowius, Marcus 2 Zinna, Md. Ali 1 Ananyevskiy, Alexey 1 Antieau, Ben 1 Banerjee, Sourjya 1 Bérczi, Gergely 1 Berrick, A. Jon 1 Bethea, Candace 1 Bhatt, Bhargav 1 Binda, Federico 1 Blanc, Anthony 1 Brazelton, Thomas 1 Bunke, Ulrich 1 Bunnett, Dominic 1 Chu, Huah 1 Dahlhausen, Christian 1 Dan-Cohen, Ishai 1 Devalapurkar, Sanath 1 Donaldson, Simon Kirwan 1 Dubouloz, Adrien 1 Ellis, Dondi 1 Feld, Niels 1 Feller, Peter 1 First, Uriya A. 1 Garibaldi, Skip 1 Garkusha, Grigory 1 Geisser, Thomas H. 1 Gepner, David 1 Gille, Stefan G. 1 Guletskiǐ, Vladimir 1 Gupta, Neena 1 Gupta, Rahul 1 Haine, Peter J. 1 Hasemeyer, Christian 1 Hausel, Tamás 1 Heller, Jeremiah 1 Hesselholt, Lars 1 Hitchin, Nigel 1 Hu, Shou-Jen 1 Huber-Klawitter, Annette 1 Iwasa, Ryomei 1 Karoubi, Max 1 Kerz, Moritz C. 1 Kirwan, Frances Clare 1 Koizumi, Junnosuke 1 Kolte, Sagar U. 1 Kong, Hana Jia 1 Krauskopf, Bernd 1 Krishna, Amalendu 1 Kuijper, Josefien 1 Kulkarni, Girish 1 Kumallagov, D. Z. ...and 44 more Authors all top 5 Cited in 51 Serials 14 Advances in Mathematics 11 Documenta Mathematica 9 Journal of Algebra 7 Journal of Pure and Applied Algebra 6 Geometry & Topology 5 Inventiones Mathematicae 5 Journal of the Institute of Mathematics of Jussieu 5 Annals of \(K\)-Theory 4 Compositio Mathematica 4 Duke Mathematical Journal 4 Transactions of the American Mathematical Society 4 Annals of Mathematics. Second Series 4 Journal of Topology 3 Mathematische Annalen 3 Mathematische Zeitschrift 3 Journal of Algebraic Geometry 3 Algebraic & Geometric Topology 3 Algebra & Number Theory 3 Forum of Mathematics, Sigma 2 Acta Mathematica Vietnamica 2 Manuscripta Mathematica 2 Journal of the American Mathematical Society 2 Journal of the Ramanujan Mathematical Society 2 The New York Journal of Mathematics 2 Journal of the European Mathematical Society (JEMS) 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications in Algebra 1 Israel Journal of Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Nagoya Mathematical Journal 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Proceedings of the Japan Academy. Series A 1 Sugaku Expositions 1 International Journal of Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Indagationes Mathematicae. New Series 1 St. Petersburg Mathematical Journal 1 Selecta Mathematica. New Series 1 Transformation Groups 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Algebra and its Applications 1 Oberwolfach Reports 1 Journal of Homotopy and Related Structures 1 Journal of \(K\)-Theory 1 Forum of Mathematics, Pi 1 Research in the Mathematical Sciences 1 European Journal of Mathematics 1 Journal de l’École Polytechnique – Mathématiques all top 5 Cited in 20 Fields 126 Algebraic geometry (14-XX) 71 \(K\)-theory (19-XX) 46 Algebraic topology (55-XX) 25 Commutative algebra (13-XX) 22 Group theory and generalizations (20-XX) 18 Number theory (11-XX) 16 Category theory; homological algebra (18-XX) 6 Nonassociative rings and algebras (17-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Associative rings and algebras (16-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Field theory and polynomials (12-XX) 3 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year