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Panin, Ivan Alexandrovich

Statistics Math-Net.Ru
Total publications: 31
Scientific articles: 27
Presentations: 37

Number of views:
This page:3552
Abstract pages:7072
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References:438
Corresponding member of RAS
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Website: http://www.pdmi.ras.ru/~panin
Keywords: algebraic K-theory, motivic cohomology, Riemann–Roch type theorems, oriented cohomology theories, linear algebraic groups, Gersten's conjecture, a conjecture of Grothendieck, purity theorems, Characteristic classes and numbers, Morava K-theories, homogeneous varieties, quadratic forms, principal homogeneous spaces.

Subject:

Algebraic K-groups of twisted forms of flag varieties and principal homogeneous spaces over semi-simple algebraic groups.Index reduction formulas for skew-fields (with A. Merkurjev, A. Wadsworth) are proved. Gersten conjecture is proved (equi-characteristic case). Purity problem for quadratic forms is solved (with M. Ojanguren). A concept of oriented cohomology theory on algebraic varieties is introduced, Riemann–Roch theorem is proved for a ring morphism of oriented theories (with A. Smirnov). An explicite formulae for the Todd genus of such a ring morphism is found. Suslin's rigidity theorem is extended (S. Yagunov) to any oriented theory.

Biography

Graded in 1981 by Department of Mathematic and Mechanic Leningrad State University. Ph.D. Theses got in 1984 from Leningrad Branch of Steklov Mathematical Institute. Defended Habilitation in 1996. Head of a laboratory in Steklov Mathematical Institute (St. Petersburg) since 1999.

Since 1995 till 1999 I was applying the technic of V. Voevodsky's article "Homology of schemes. II" to a conjecture of Grothendieck (with Suslin and Ojanguren) and to purity problems (with Ojanguren). Since 1999 I began to transplant (with A. Smirnov) the concept of oriented cohomology theory (to algebra from topology). The notion has been fixed, for a ring morphism of oriented theories an explicite formulae for Todd genus is given and a Riemann–Roch theorem is proved. With S. Yagunov the rigidity theorem of A. Suslin was extended to an oriented theory. Now a variant of Poincare duality is working out.

   
Main publications:
  • Panin I. A. On the algebraic $K$-theory of twisted flag varieties // K-Theory 8 (1994), no. 6, 541–585.
  • Merkurjev A. S., Panin I. A., Wadsworth A. R. Index reduction formulas for twisted flag varieties. I // K-Theory 10 (1996), no. 6, 517–596.
  • Panin I. A. Splitting principle and K-theory of simply connected semisimple algebraic groups. (Russian) Algebra i Analiz 10 (1998), no. 1, 88–131; translation in St. Petersburg Math. J. 10 (1999), no. 1, 69–101.
  • Ojanguren M., Panin I. A purity theorem for the Witt group // Ann. Sci. Ecole Norm. Sup. (4) 32 (1999), no. 1, 71–86.
  • Panin I., Smirnov A. Push-forwards in oriented cohomology theories of algebraic varieties. Preprint http://www.math.uiuc.edu/K-theory/0459/index.html.

http://www.mathnet.ru/eng/person17453
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/238161
http://elibrary.ru/author_items.asp?authorid=7690

Publications in Math-Net.Ru
2020
1. I. A. Panin, “Proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing a field”, Izv. RAN. Ser. Mat., 84:4 (2020),  169–186  mathnet; Izv. Math., 84:4 (2020), 780–795  isi
2019
2. I. A. Panin, “Nice triples and moving lemmas for motivic spaces”, Izv. RAN. Ser. Mat., 83:4 (2019),  158–193  mathnet  elib; Izv. Math., 83:4 (2019), 796–829  isi  scopus
3. I. A. Panin, C. Walter, “On the Relation of Symplectic Algebraic Cobordism to Hermitian $K$-Theory”, Tr. Mat. Inst. Steklova, 307 (2019),  180–192  mathnet  elib; Proc. Steklov Inst. Math., 307 (2019), 162–173  isi  scopus
4. I. Panin, “A short exact sequence”, Zap. Nauchn. Sem. POMI, 485 (2019),  176–186  mathnet
5. I. Panin, “Notes on a Grothendieck–Serre conjecture in mixed characteristic case”, Zap. Nauchn. Sem. POMI, 484 (2019),  138–148  mathnet
6. I. A. Panin, “A short proof of a theorem due to O. Gabber”, Zap. Nauchn. Sem. POMI, 479 (2019),  131–136  mathnet
2018
7. I. Panin, C. Walter, “On the motivic commutative ring spectrum $\mathbf{BO}$”, Algebra i Analiz, 30:6 (2018),  43–96  mathnet  mathscinet  elib; St. Petersburg Math. J., 30:6 (2019), 933–972  isi  scopus
2017
8. I. A. Panin, “A moving lemma for motivic spaces”, Algebra i Analiz, 29:6 (2017),  178–181  mathnet  mathscinet  elib; St. Petersburg Math. J., 29:6 (2018), 993–995  isi
2016
9. I. A. Panin, “On Grothendieck–Serre's conjecture concerning principal $G$-bundles over reductive group schemes: II”, Izv. RAN. Ser. Mat., 80:4 (2016),  131–162  mathnet  mathscinet  zmath  elib; Izv. Math., 80:4 (2016), 759–790  isi  scopus
10. I. A. Panin, A. K. Stavrova, “On the Grothendieck–Serre conjecture concerning principal $G$-bundles over semi-local Dedekind domains”, Zap. Nauchn. Sem. POMI, 443 (2016),  133–146  mathnet  mathscinet; J. Math. Sci. (N. Y.), 222:4 (2017), 453–462  scopus
2015
11. I. Panin, K. Pimenov, “Rationally isotropic quadratic spaces are locally isotropic. III”, Algebra i Analiz, 27:6 (2015),  234–241  mathnet  mathscinet  elib; St. Petersburg Math. J., 27:6 (2016), 1029–1034  isi  scopus
12. I. A. Panin, K. I. Pimenov, “A variant of the Levine–Morel moving Lemma”, Zap. Nauchn. Sem. POMI, 435 (2015),  163–167  mathnet  mathscinet; J. Math. Sci. (N. Y.), 219:4 (2016), 595–597
2009
13. I. A. Panin, S. A. Yagunov, “Duality theorem for motives”, Algebra i Analiz, 21:2 (2009),  205–213  mathnet  mathscinet  zmath; St. Petersburg Math. J., 21:2 (2010), 309–315  isi  scopus
2007
14. I. Panin, U. Rehmann, “A variant of a theorem by Springer”, Algebra i Analiz, 19:6 (2007),  117–125  mathnet  mathscinet  zmath; St. Petersburg Math. J., 19:6 (2008), 953–959  isi
2003
15. I. A. Panin, “The Equicharacteristic Case of the Gersten Conjecture”, Tr. Mat. Inst. Steklova, 241 (2003),  169–178  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 241 (2003), 154–163
2000
16. I. A. Panin, A. L. Smirnov, “On a theorem of Grothendieck”, Zap. Nauchn. Sem. POMI, 272 (2000),  286–293  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 116:1 (2003), 3042–3046
1998
17. I. A. Panin, “Splitting principle and $K$-theory of simply connected semisimple algebraic groups”, Algebra i Analiz, 10:1 (1998),  88–131  mathnet  mathscinet  zmath; St. Petersburg Math. J., 10:1 (1999), 68–101
1997
18. I. A. Panin, A. A. Suslin, “On a conjecture of Grothendieck concerning Azumaya algebras”, Algebra i Analiz, 9:4 (1997),  215–223  mathnet  mathscinet  zmath; St. Petersburg Math. J., 9:4 (1998), 851–858
1991
19. I. A. Panin, “A splitting principle and the algebraic $K$-theory of some homogeneous varieties”, Zap. Nauchn. Sem. LOMI, 198 (1991),  49–64  mathnet  mathscinet  zmath; J. Soviet Math., 64:1 (1993), 737–750
1989
20. I. A. Panin, “Stabilization for orthogonal and symplectic algebraic $K$-theories”, Algebra i Analiz, 1:3 (1989),  172–195  mathnet  mathscinet  zmath; Leningrad Math. J., 1:3 (1990), 741–764
21. I. A. Panin, “Algebraic $K$-theory of Grassmann varieties and their convoluted forms”, Funktsional. Anal. i Prilozhen., 23:2 (1989),  71–72  mathnet  mathscinet  zmath; Funct. Anal. Appl., 23:2 (1989), 143–144  isi
22. I. A. Panin, “Comparison of Quillen's and Volodin's $K$-theories”, Zap. Nauchn. Sem. LOMI, 175 (1989),  93–105  mathnet  mathscinet  zmath; J. Soviet Math., 57:6 (1991), 3500–3507
1987
23. I. A. Panin, “Homological stabilization for the symplectic and orthogonal groups”, Zap. Nauchn. Sem. LOMI, 160 (1987),  222–228  mathnet  zmath
1986
24. I. A. Panin, “On a theorem of Hurewicz and $K$-theory of complete discrete valuation rings”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986),  763–775  mathnet  mathscinet  zmath; Math. USSR-Izv., 29:1 (1987), 119–131
1982
25. I. A. Panin, “Fields with vanishing $K_2$. Torsion in $H^1(X,K_2)$ and $Ch^2(X)$”, Zap. Nauchn. Sem. LOMI, 116 (1982),  108–118  mathnet  mathscinet  zmath; J. Soviet Math., 26:3 (1984), 1901–1908
1980
26. I. A. Panin, “Rationality of bundles of conies with a degeneration curve of degree five and even theta-characteristic”, Zap. Nauchn. Sem. LOMI, 103 (1980),  100–105  mathnet  mathscinet  zmath; J. Soviet Math., 24:4 (1984), 449–452

2018
27. A. A. Beilinson, A. S. Vishik, D. A. Kazhdan, M. M. Kapranov, A. S. Merkurjev, D. O. Orlov, I. A. Panin, A. A. Suslin, N. A. Tyurin, G. B. Shabat, “Vladimir Aleksandrovich Voevodsky (obituary)”, Uspekhi Mat. Nauk, 73:3(441) (2018),  157–168  mathnet  elib; Russian Math. Surveys, 73:3 (2018), 519–531  isi
2015
28. D. G. Benua, M. V. Bondarko, N. A. Vavilov, M. A. Vsemirnov, A. I. Generalov, N. L. Gordeev, I. B. Zhukov, G. A. Leonov, B. B. Lur'e, I. A. Panin, A. L. Smirnov, I. B. Fesenko, A. V. Yakovlev, “To the anniversary of Sergei Vladimirovich Vostokov”, Algebra i Analiz, 27:6 (2015),  3–5  mathnet  mathscinet  elib; St. Petersburg Math. J., 27:6 (2016), 861–862  isi  scopus
2014
29. N. A. Vavilov, È. B. Vinberg, I. A. Panin, A. N. Panov, A. N. Parshin, V. P. Platonov, V. L. Popov, “Valentin Evgen'evich Voskresenskii (obituary)”, Uspekhi Mat. Nauk, 69:4(418) (2014),  177–178  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 69:4 (2014), 753–754  isi
2000
30. N. A. Vavilov, S. V. Vostokov, A. I. Generalov, N. L. Gordeev, B. B. Lur'e, A. S. Merkur'ev, V. V. Ishkhanov, I. A. Panin, A. I. Skopin, A. A. Suslin, “Anatolii Vladimirovich Yakovlev”, Zap. Nauchn. Sem. POMI, 272 (2000),  5–13  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 116:1 (2003), 2883–2886

Presentations in Math-Net.Ru
1. Motivic version of Segal's machinery
I. A. Panin
SIMC Open
December 25, 2019 12:20   
2. О топологическом аналоге гипотезы Гротендика–Серра, занятие 4
I. A. Panin
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 25, 2018 11:15   
3. О топологическом аналоге гипотезы Гротендика–Серра, занятие 3
I. A. Panin
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 24, 2018 15:30   
4. О топологическом аналоге гипотезы Гротендика–Серра, занятие 2
I. A. Panin
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 22, 2018 11:15   
5. О топологическом аналоге гипотезы Гротендика–Серра, занятие 1
I. A. Panin
Summer School "Contemporary Mathematics" named Vitaly Arnold, 2018
July 21, 2018 17:15   
6. Об оснащенных соответствиях Воеводского
I. Panin
One-day conference dedicated to the memory of Vladimir A. Voevodsky
December 28, 2017 12:40   
7. Об одной гипотезе Гротендика–Серра. Занятие 4
I. A. Panin
XVII Summer School "Contemporary Mathematics", 2017
July 27, 2017 15:30   
8. Об одной гипотезе Гротендика–Серра. Занятие 3
I. A. Panin
XVII Summer School "Contemporary Mathematics", 2017
July 24, 2017 11:15   
9. Об одной гипотезе Гротендика–Серра. Занятие 2
I. A. Panin
XVII Summer School "Contemporary Mathematics", 2017
July 22, 2017 15:30   
10. Об одной гипотезе Гротендика–Серра. Занятие 1
I. A. Panin
XVII Summer School "Contemporary Mathematics", 2017
July 21, 2017 09:30   
11. Around the Grothendieck–Serre conjecture on principal $G$-bundles
Ivan Panin
International conference "Algebraic Groups and Lie Groups" on the occasion of the 70th birthday of Vladimir L. Popov
October 4, 2016 15:00   
12. Введение в $А^1$-гомотопическую теорию Мореля–Воеводского. Занятие 4
I. A. Panin
Summer School "Contemporary Mathematics", 2016
July 27, 2016 11:15   
13. Введение в $А^1$-гомотопическую теорию Мореля–Воеводского. Занятие 3
I. A. Panin
Summer School "Contemporary Mathematics", 2016
July 26, 2016 15:30   
14. Введение в $А^1$-гомотопическую теорию Мореля–Воеводского. Занятие 2
I. A. Panin
Summer School "Contemporary Mathematics", 2016
July 24, 2016 11:15   
15. Введение в $A^1$-гомотопическую теорию Мореля–Воеводского. Занятие 1
I. A. Panin
Summer School "Contemporary Mathematics", 2016
July 22, 2016 11:15   
16. Ещё раз о гипотезе Гротендика–Серра
I. A. Panin
One-day conference dedicated to the memory of V. A. Iskovskikh
December 29, 2015 15:40   
17. Мотивные когомологии. Занятие 4
I. A. Panin
Summer School "Contemporary Mathematics", 2015
July 28, 2015 09:30   
18. Мотивные когомологии. Занятие 3
I. A. Panin
Summer School "Contemporary Mathematics", 2015
July 25, 2015 15:30   
19. Мотивные когомологии. Занятие 2
I. A. Panin
Summer School "Contemporary Mathematics", 2015
July 22, 2015 15:30   
20. Мотивные когомологии. Занятие 1
I. A. Panin
Summer School "Contemporary Mathematics", 2015
July 19, 2015 11:15   
21. Линейные frame-мотивы
I. A. Panin
Traditional winter session MIAN–POMI
December 20, 2014 10:00   
22. Теорема Дольда–Тома, гомологии Суслина и введение в мотивные гомологии и когомологии Воеводского. Лекция 4
I. A. Panin
Summer School "Contemporary Mathematics", 2014
July 28, 2014 17:00   
23. Теорема Дольда–Тома, гомологии Суслина и введение в мотивные гомологии и когомологии Воеводского. Лекция 3
I. A. Panin
Summer School "Contemporary Mathematics", 2014
July 26, 2014 11:15   
24. Теорема Дольда–Тома, гомологии Суслина и введение в мотивные гомологии и когомологии Воеводского. Лекция 2
I. A. Panin
Summer School "Contemporary Mathematics", 2014
July 22, 2014 09:30
25. Теорема Дольда–Тома, гомологии Суслина и введение в мотивные гомологии и когомологии Воеводского. Лекция 1
I. A. Panin
Summer School "Contemporary Mathematics", 2014
July 20, 2014 11:15   
26. A proof of the geometric case of a conjecture of Grothendieck and Serre concerning principal bundles
I. A. Panin
International conference "Geometry of Algebraic Varieties" dedicated to the memory of V. A. Iskovskikh
October 24, 2013 15:00   
27. Rationally isotropic quadratic forms are locally isotropic
I. Panin
Annual memorial conference dedicated to the memory of Andrei Nikolaevich Tyurin (24.02.1940–27.10.2002) "Algebraic and Differential Geometry of Andrei Tyurin"
October 25, 2012 11:15   
28. Algebraic cobordisms and their applications. Lecture 4
I. A. Panin
Summer School "Contemporary Mathematics", 2012
July 29, 2012 17:00   
29. Algebraic cobordisms and their applications. Lecture 3
I. A. Panin
Summer School "Contemporary Mathematics", 2012
July 27, 2012 11:15   
30. Algebraic cobordisms and their applications. Lecture 2
I. A. Panin
Summer School "Contemporary Mathematics", 2012
July 24, 2012 15:30   
31. Algebraic cobordisms and their applications. Lecture 1
I. A. Panin
Summer School "Contemporary Mathematics", 2012
July 23, 2012 15:30   
32. Популярное введение в $A^1$-гомотопическую теорию Воеводского и Мореля
I. A. Panin
Meetings of the Moscow Mathematical Society
November 1, 2011 18:30
33. Об одной гипотезе Колье–Телена для квадрик
I. A. Panin
Seminar by Algebra Department
December 15, 2009 15:00
34. О гипотезе Гротендика–Серра про главные $G$-расслоения, где $G$ – полупростая группа
I. A. Panin
Seminar by Algebra Department
May 26, 2009 15:00
35. Riemann-Roch type theorems
I. A. Panin
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
March 11, 2002
36. Вариации на тему работ Воеводского по гипотезе Милнора
I. A. Panin
General Mathematics Seminar of the St. Petersburg Division of Steklov Institute of Mathematics, Russian Academy of Sciences
October 19, 1998
37. Four squares and the Grothendieck conjecture
I. A. Panin
Meetings of the St. Petersburg Mathematical Society
October 13, 1998

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