Zinovy Reichstein

Professor of Mathematics

University of British Columbia

Publications and Preprints

  1. Zinovy Reichstein, Hilbert's 13th Problem for algebraic groups, submitted for publication. Posted April 2022.

  2. Zinovy Reichstein, Federico Scavia, The behavior of essential dimension under specialization II, submitted for publication. Posted December 2021.

  3. Zinovy Reichstein, Federico Scavia, The behavior of essential dimension under specialization, submitted for publication. Posted December 2021.

  4. Zinovy Reichstein, From Hilbert's 13th Problem to essential dimension and back, European Mathematical Society Magazine, No. 122 (2021), 4-15. Posted November 2021.
    Preprint version
    Published version

  5. Zhengheng Bao, Zinovy Reichstein, A non-commutative Nullstellensatz, to appear in Journal of Algebra and Applications. Posted August 2021.

  6. Uriya A. First, Zinovy Reichstein, Ben Williams , On the number of generators of an algebra over a commutative ring , submitted for publication. Posted December 2020.

  7. Matthew Brassil, Zinovy Reichstein, On the number of symmetric presentations of a determinantal hypersurface, Linear Algebra and its Applications 617 (2021), no. 15, 39-48.

  8. Matthew Brassil, Zinovy Reichstein, A graph-theoretic approach to a conjecture of Dixon and Pressman, to appear in Israel Journal of Mathematics. Posted October 2020.

  9. Tran-Trung Nghiem, Zinovy Reichstein, On a rationality problem for fields of cross-ratios II. Canadian Mathematical Bulletin, 64(3), 667-677. doi:10.4153/S0008439520000739
    Preprint version
    Published version

  10. Zinovy Reichstein, Federico Scavia, On the essential dimension of an algebraic group whose connected component is a torus, Algebraic Geometry 8 (6), 2021, 749-769 (2021).

    Preprint version

    Published version

  11. Mathieu Florence, Norbert Hoffmann , Zinovy Reichstein, The rationality problem for forms of moduli spaces of stable marked curves of positive genus , Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) Vol. XXII (2021), 1091-1104.

  12. Zinovy Reichstein, Dajano Tossici, Special groups, versality and the Grothendieck-Serre conjecture, Doc. Math. 25, 171-188 (2020).

  13. Zinovy Reichstein, Abhishek Kumar Shukla, Essential dimension of double covers of symmetric and alternating groups, Journal of the Ramanujan Mathematical Society, 35 (2020), no. 4, 357-372.

  14. Zinovy Reichstein, Federico Scavia, The Noether Problem for spinor groups of small rank, Preprint version, Published version: Journal of Algebra 548 (2020), 134-152.

  15. Zinovy Reichstein, On a rationality problem for fields of cross-ratios, Tokyo J. Math. 43 (2020), no. 1, 205-213.
    Preprint version.
    Published version.

  16. Matthew Brassil, Zinovy Reichstein, Hermite's theorem via Galois cohomology, Archiv der Mathematik, 112 (2019), no. 5, 467-473.

  17. Zinovy Reichstein, Abhishek Kumar Shukla, Essential dimension of inseparable field extensions, Algebra Number Theory 13 (2019), no. 2, 513-530.

  18. Jim Bryan, Samuel Leutheusser, Zinovy Reichstein, Mark Van Raamsdonk, Locally Maximally Entangled States of Multipart Quantum Systems, Quantum 3, 115 (2019).

  19. Zinovy Reichstein, The Jordan property of Cremona groups and essential dimension, Archiv der Mathematik 111 (2018), no. 5, 449-455.

  20. P. Brosnan, Z. Reichstein, A. Vistoli, Essential dimension in mixed characteristic, Doc. Math. 23, 1587-1600 (2018).
    ArXIV version
    Published version

  21. Zinovy Reichstein, Angelo Vistoli, Essential dimension of finite groups in prime characteristic, Comptes Rendus Math. Acad. Sci. Paris 356 (2018), no. 5, 463-467.

  22. Uriya First, Zinovy Reichstein, and Santiago Salazar, On the number of generators of a separable algebra over a finite field. Posted September, 2017.

  23. Jim Bryan, Zinovy Reichstein, and Mark Van Raamsdonk, Existence of locally maximally entangled quantum states via geometric invariant theory, Annales Henri Poincare, (2018), no. 8, 2491-2511.

  24. Mathieu Florence, Zinovy Reichstein, The rationality problem for forms of moduli spaces of stable curves of genus 0, Bulletin of the London Math. Society, Volume 50, no. 1, February 2018, 148-158.

  25. Dave Benson, Zinovy Reichstein, Fields of definition for representations of associative algebras, Proceedings of the Edinburgh Mathematical Society, Volume 62, Issue 1, 2019, 291-304

  26. Zinovy Reichstein, On a property of real plane curves of even degree, Canadian Math. Bulletin, Volume 62, Issue 1, March 2019 , pp. 179-182.

  27. Uriya First, Zinovy Reichstein, On the number of generators of an algebra, Comptes Rendus Mathematique, Volume 355, no. 1 (2017), 5-9.

  28. Jason Bell, Dragos Ghioca, Zinovy Reichstein, Matthew Satriano, On the Medvedev-Scanlon conjecture for minimal threefolds of non-negative Kodaira Dimension, New York J. Math. 23 (2017), 1185--1203.

  29. Uriya First, Zinovy Reichstein, On the number of generators of an algebra, Comptes Rendus Mathematique, Volume 355, no. 1 (2017), 5-9.

  30. Z. Reichstein, A. Vistoli, On the dimension of the locus of determinantal hypersurfaces, Canadian Math. Bulletin 60 (2017), no. 3, 613-630.

  31. Matthew Brassil, Zinovy Reichstein, The Hermite-Joubert problem over p-fields, 2015 Clifford Lectures on Algebraic Groups: Structure and Actions, Contemporary Mathematics, vol. 94, edited by Michel Brion and Mahir Bilen Can, American Mathematical Society, 2017, 31-52. Note that conjectures 14.1 and 14.3 were recently proved by Khoa Nguyen.

  32. Shane Cernele, Zinovy Reichstein, Essential dimension and linear codes, with an appendix by Athena Nguyen. Pacific Journal of Mathematics 279-1 (2015), 155-179.

  33. Jason Bell, Dragos Ghioca, Zinovy Reichstein, On a dynamical version of a theorem of Rosenlicht, Ann. Sc. Norm. Super. Pisa Cl. Sci., Volume XVII, no. 1, 2017, 187-204 .

  34. Nikita Karpenko, Zinovy Reichstein, A numerical invariant for linear representations of finite groups, with an appedix by Julia Pevtsova and Zinovy Reichstein. Commentarii Math. Helveciti, Volume 90, no. 3, 2015, 667-701.

  35. Z. Reichstein, Joubert's theorem fails in characteristic 2, C. R. Math. Acad. Sci. Paris 352 (2014), no. 10, 773-777.

  36. M. Borovoi, N. Lemire, B. Kunyavskii, Z. Reichstein, Stably Cayley groups in characteristic zero, Int. Math. Res. Notices, No. 19, 5340-5397 (2014).

  37. D. Anderson, M. Florence, Z. Reichstein, The Lie algebra of type G_2 is rational over its quotient by the adjoint action, C. R. Math. Acad. Sci. Paris 351 (2013), no. 23-24, 871-875.

  38. A. Duncan, Z. Reichstein, Pseudo-reflection groups and essential dimension, Lond. Math. Soc., II. Ser. 90, No. 3, 879-902 (2014).

  39. Z. Reichstein, Introduction to the theory of essential dimension. Lecture notes for the mini-course given at the Spring School on Torsors, Motives and Cohomological Invariants at the Fields Institute, May 2013.

  40. R. Lötscher, A. Meyer, M. MacDonald, Z. Reichstein, Essential p-dimension of algebraic groups whose connected component is a torus, Algebra Number Theory 7 (2013), no. 8, 1817-1840.

  41. A. Duncan, Z. Reichstein, Versality of algebraic group actions and rational points on twisted varieties. J. Algebraic Geom. 24 (2015), 499-530.

  42. R. Lötscher, A. Meyer, M. MacDonald, Z. Reichstein, Essential dimension of algebraic tori, J. Reine Angew. Math. (Crelle's Journal), 677 (2013), 1-13.

  43. Z. Reichstein, A. Vistoli, A genericity theorem for algebraic stacks and essential dimension of hypersurfaces, Journal of the European Math. Society (JEMS), 15 (2013), no. 6, 1999-2026.

  44. Z. Reichstein, What is ... essential dimension?, Notices of the AMS, vol. 59, no. 10 (2012), 1432-1434.

  45. J.-L. Colliot-Thelene, B. Kunyavskii, V. L. Popov, Z. Reichstein, Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?, Compositio Mathematica, vol. 147 (2011), no. 2, 428-466.

  46. M. Borovoi, Z. Reichstein, Toric-friendly groups, Algebra and Number Theory, vol. 5 (2011), no. 3, 361-378.

  47. S. Cernele, M. Kamgarpour, Z. Reichstein, Maximal representation dimension for groups of order p^n, Journal of Group Theory, vol. 14 (2011), no. 4, 637-647.

  48. A. Meyer, Z. Reichstein, An upper bound on the essential dimension of a central simple algebra, Journal of Algebra, vol. 329, issue 1 (Special Issue Celebrating the 60th Birthday of Corrado De Concini), March 2011, 213-221.

  49. P. Brosnan, Z. Reichstein, A. Vistoli, Essential dimension of moduli of curves and other algebraic stacks, with an appendix by Najmuddin Fakhruddin, Journal of the European Math. Society (JEMS) 13 (2011), no. 4, 1079-1112.

  50. Z. Reichstein, Essential dimension, Proceedings of the International Congress of Mathematicians, vol. II, 162-188, Hindustan Book Agency, New Delhi, 2010.

  51. A. Adem, Z. Reichstein, Bundles, cohomology and truncated symmetric polynomials, Documenta Math. 15 (2010), 1029-1047.

  52. A. Meyer, Z. Reichstein, Some consequences of the Karpenko-Merkurjev theorem, Documenta Math. Extra vol.: Andrei A. Suslin's Sixtieth Birthday (2010), 445-457. Posted November 2008.

  53. A. Meyer, Z. Reichstein, The essential dimension of the normalizer of a maximal torus in the projective linear group, Algebra and Number Theory, vol. 3 (2009), no. 4, 467-487.

  54. P. Brosnan, Z. Reichstein, A. Vistoli, Essential dimension, spinor groups and quadratic forms, Annals of Math., vol. 171 (2010), no. 1, 533-544.

  55. A. Duncan, Z. Reichstein, SAGBI bases in rings of invariant Laurent polynomials, Proceedings of the American Mathematical Society 137 (2009), no. 3, 835-844. Posted February 2008.

  56. V. Chernousov, Ph. Gille, Z. Reichstein, Reduction of structure for torsors over semilocal rings, Manuscripta. Math 126 (2008), 465-480.

  57. Ph. Gille, Z. Reichstein, A lower bound on the essential dimension of a connected linear group, Comment. Math. Helv. 84, no. 1, 189-212 (2009). Posted March 2007.

  58. Z. Reichstein, N. Vonessen, Tame group actions on central simple algebras, J. Algebra, 318 (2007), no. 2, 1039-1056.

  59. P. Brosnan, Z. Reichstein, A. Vistoli, Essential dimension and algebraic stacks. Posted February 2007.

  60. J. Kuttler, Z. Reichstein, Is the Luna startification intrinsic? in Annales de l'Institut Fourier (Grenoble) 58 (2008), no. 2, 689-721. Posted October 2006.

  61. N. Lemire, V. L. Popov, Z. Reichstein, On the Cayley degree of an algebraic group, Biblioteca de la Revista Matematica Iberoamericana, Actas del XVI Coloquio Latinoamericana de A'lgebra, Madrid, 2007, 87-97. Posted August 2006.

  62. Z. Reichstein, A note on retracts and lattices (after D. J. Saltman). Posted March 2006.

  63. Z. Reichstein, Higher trace forms and essential dimension in central simple algebras, Archiv der Mathematik, 88, no. 1 (2007), 12-18. Posted March 2006.

  64. Z. Reichstein, N. Vonessen , Group actions and invariants in algebras of generic matrices, Advances in Applied Mathematics 37, issue 4, October 2006, 481-500.

  65. A. Vistoli, Z. Reichstein Birational isomorphisms between twisted group actions, Journal of Lie Theory 16 (2006), no. 4, 791-802.

  66. N. Lemire, V. L. Popov, Z. Reichstein, Cayley groups, J. Amer. Math. Soc. 19 (2006), 921-967.

  67. Z. Reichstein, N. Vonessen, Group actions on central simple algebras: a geometric approach, J. Algebra 304 (2006), 1160-1192.

  68. Z. Reichstein, N. Vonessen, Polynomial identity rings as rings of functions, Journal of Algebra, 310, issue 2 (2007), 624-647.

  69. G. Berhuy, Z. Reichstein, On the notion of canonical dimension for algebraic groups, Advances in Mathematics, 198 (2005), 128-171.

  70. V. Chernousov, Ph. Gille, Z. Reichstein, Resolving G-torsors by abelian base extensions, Journal of Algebra 296 (2006), 561-581.

  71. Z. Reichstein, D. Rogalski, J. J. Zhang, Projectively simple rings, Advances in Mathematics, 203 (2006), no. 2, 365-407.

  72. C. DeConcini , Z. Reichstein, Nesting maps of Grassmannians, Rendiconti di Matematica Accademia dei Lincei, s. 9, v. 15 (2004), 109-118.

  73. C. U. Jensen, A. Ledet, N. Yui, Generic Polynomials, constructive aspects of Galois theory, MSRI Publications, Cambridge University Press, 2002. Book review by Z. Reichstein, Canadian Math. Society Notes, vol. 35, no. 8 (2003), 12-13.

  74. Z. Reichstein, N. Vonessen, Stable affine models for algebraic group actions, Journal of Lie Theory, 14, no. 2 (2004), 563-568.

  75. J. Minac, Z. Reichstein, Trace forms of Galois extensions in the presence of a 4th root of unity, International Math. Research Notices, 8 (2004), 389-410.

  76. J. Buhler, Z. Reichstein, Symmetric functions and the phase problem in crystallography, Transactions of the American Math. Society, 357 (2005), 2353-2377.

  77. Z. Reichstein, Compressions of group actions, 199-202, CRM Proc. Lecture Notes, 35, Amer. Math. Soc., Providence, RI, 2004.

  78. Z. Reichstein, B. Youssin, A non-split torsor with trivial fixed point obstruction, Journal of Algebra, 263 (2003), 255-261.

  79. Z. Reichstein, SAGBI bases in rings of multiplicative invariants, Commentarii Math Helvitici 78 (2003), 185- 202.

  80. M. Lorenz, Z. Reichstein, L.H. Rowen, D. J. Saltman, Fields of definition for division algebras, Journal of the London Mathematical Society, 68, issue 03 (2003), 651-670.

  81. D.-S. Kang, Z. Reichstein, Trace forms of Galois field extensions in the presence of roots of unity, J. Reine Angew. Math. (Crelle's Journal), 549 (2002), 79-89.

  82. Z. Reichstein, B. Youssin, A birational invariant for algebraic group actions, Pacific Jounal of Mathematics, 204, no. 1 (2002), 223-246.

  83. Z. Reichstein, B. Youssin, Equivariant resolution of points of indeterminacy, Proceedings AMS, vol. 130, no. 8, 2183-2187.

  84. Z. Reichstein, B. Youssin, Conditions satisfied by characteristic polynomials in fields and division algebras, Journal of Pure and Applied Algebra, 166 (2002), 165-184.

  85. M. Lorenz, Z. Reichstein, Lattices and parameter reduction in division algebras, MSRI preprint, January 2000.

  86. Z. Reichstein, An inductive proof of Newton's identities (in Russian), Matematicheskoe Prosveschenie [Mathematics Education], 3, (4) (2000), 204-205.

  87. Z. Reichstein, B. Youssin, On a property of special groups , Transformation Groups, 6, no. 3 (2001), 261-266.

  88. Z. Reichstein, B. Youssin, Parusinski's "Key Lemma" via algebraic geometry, Electronic Research Announcements of the AMS, vol. 5 (1999), 136-145.

  89. Z. Reichstein, B. Youssin, Splitting fields of G-varieties, Pacific Journal of Mathematics, 200 (2001), 207-249.

  90. Z. Reichstein, B. Youssin, Essential dimensions of algebraic groups and a resolution theorem for G-varieties, with an appendix by J. Kollar and E. Szabo, Canadian Journal of Mathematics, 52, no. 5 (2000), 1018-1056.

  91. Z. Reichstein, On the notion of essential dimension for algebraic groups, Transformation Groups, 5, no. 3 (2000), 265-304.

  92. Z. Reichstein, On a theorem of Hermite and Joubert, Canadian Journal of Mathematics, 51(1), 1999, 69-95.

  93. J. Buhler, Z. Reichstein, On Tschirnhaus transformations, in Topics in Number Theory, edited by S. D. Ahlgren et al., Kluwer Academic Publishers, 1999, 127-142.

  94. L. LeBruyn, Z. Reichstein, Smoothness in algebraic geography, Proceedings of the London Math. Society, (3) 79, July 1999, 158-191.

  95. Z. Reichstein, Generators of central simple algebras, Journal of Algebra, 207 (1998), 511-524.

  96. J. Buhler, Z. Reichstein, On the essential dimension of a finite group, Compositio Math. 106 (1997), 159-179.

  97. Z. Reichstein, N. Vonessen, Rational central simple algebras, Israel J. of Math. 95 (1996), 253-280.

  98. Z. Reichstein, On a question of Makar-Limanov, Proc. AMS, 124, no. 1 (1996), 17-19.

  99. Z. Reichstein, N. Vonessen, An Embedding property of universal division algebras, J. Algebra, 177 (1995), 451-462.

  100. Z. Reichstein, N. Vonessen, Free subgroups of division algebras, Comm. in Algebra, 23(6) (1995), 2181-2185.

  101. Z. Reichstein, N. Vonessen, Torus actions on rings, J. Algebra, 170(3) (1994), 781-804.

  102. Z. Reichstein, On the Noether problem and universal division algebras, Teoria dos Aneis, Proceedings of the Ring Theory Conference at the University of Sao Paulo, H. Merklen, Ed., IME. USP Publication (1993), 41-50.

  103. Z. Reichstein, On automorphisms of matrix invariants induced from the trace ring, Linear Algebra Appl., 193 (1993), 51-74.

  104. B. Reichstein, Z. Reichstein, On Waring presentations of smooth plane cubics, Michigan Math. Journal, 40(1) (1993), 95-118.

  105. Z. Reichstein, On automorphisms of matrix invariants, Transactions AMS, 340(1) (1993), 353-371.

  106. Z. Reichstein, On Waring presentations of cuspidal cubics, Comm. in Algebra, 20(11) (1992), 3347-3351.

  107. Z. Reichstein, A Functorial interpretation of the ring of matrix invariants, Journal of Algebra, 126(3) (1991), 439-462.

  108. Z. Reichstein, Stability and equivariant maps, Invent. Math. 96 (1989), 349-383.

  109. A. E. Brouwer, Z. Reichstein, E. C. Posner, Hadamard codes which have an even number of ones in each half, Utilitas Mathematica, 32 (1987), 131-140.

  110. Z. Reichstein, E. C. Posner, Configurations for file transfer protocol error protection, IEEE Transactions on Communications, vol. com-34, 3, March 1986.