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.
I. A. Panin, D. N. Tyurin, “Pfister forms and a conjecture due to Colliot–Thélène in the mixed characteristic case”, Izv. RAN. Ser. Mat., 88:5 (2024), 174–186; Izv. Math., 88:5 (2024), 977–987
2023
2.
G. A. Garkusha, I. A. Panin, P. Østvær, “Framed motivic $\Gamma$-spaces”, Izv. RAN. Ser. Mat., 87:1 (2023), 3–32; Izv. Math., 87:1 (2023), 1–28
Andrei E. Druzhinin, Ivan A. Panin, “Surjectivity of the Étale Excision Map for Homotopy Invariant Framed Presheaves”, Trudy Mat. Inst. Steklova, 320 (2023), 103–127; Proc. Steklov Inst. Math., 320 (2023), 91–114
G. Garkusha, I. Panin, “Triangulated categories of framed bispectra and framed motives”, Algebra i Analiz, 34:6 (2022), 135–169; St. Petersburg Math. J., 34:6 (2023), 991–1017
I. Panin, C. Walter, “On the algebraic cobordism spectra $\mathbf{MSL}$ and $\mathbf{MSp}$”, Algebra i Analiz, 34:1 (2022), 144–187; St. Petersburg Math. J., 34:1 (2023), 109–141
I. Panin, C. Walter, “Quaternionic Grassmannians and Borel classes in algebraic geometry”, Algebra i Analiz, 33:1 (2021), 136–193; St. Petersburg Math. J., 33:1 (2022), 97–140
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; Izv. Math., 84:4 (2020), 780–795
I. A. Panin, “Two purity theorems and the Grothendieck-Serre conjecture concerning principal $\mathbf G$-bundles”, Mat. Sb., 211:12 (2020), 123–142; Sb. Math., 211:12 (2020), 1777–1794
I. A. Panin, C. Walter, “On the Relation of Symplectic Algebraic Cobordism to Hermitian $K$-Theory”, Trudy Mat. Inst. Steklova, 307 (2019), 180–192; Proc. Steklov Inst. Math., 307 (2019), 162–173
I. Panin, “A short exact sequence”, Zap. Nauchn. Sem. POMI, 485 (2019), 176–186
15.
I. Panin, “Notes on a Grothendieck–Serre conjecture in mixed characteristic case”, Zap. Nauchn. Sem. POMI, 484 (2019), 138–148
16.
I. A. Panin, “A short proof of a theorem due to O. Gabber”, Zap. Nauchn. Sem. POMI, 479 (2019), 131–136
2018
17.
I. Panin, C. Walter, “On the motivic commutative ring spectrum $\mathbf{BO}$”, Algebra i Analiz, 30:6 (2018), 43–96; St. Petersburg Math. J., 30:6 (2019), 933–972
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; J. Math. Sci. (N. Y.), 222:4 (2017), 453–462
I. Panin, K. Pimenov, “Rationally isotropic quadratic spaces are locally isotropic. III”, Algebra i Analiz, 27:6 (2015), 234–241; St. Petersburg Math. J., 27:6 (2016), 1029–1034
I. A. Panin, K. I. Pimenov, “A variant of the Levine–Morel moving Lemma”, Zap. Nauchn. Sem. POMI, 435 (2015), 163–167; J. Math. Sci. (N. Y.), 219:4 (2016), 595–597
2009
23.
I. A. Panin, S. A. Yagunov, “Duality theorem for motives”, Algebra i Analiz, 21:2 (2009), 205–213; St. Petersburg Math. J., 21:2 (2010), 309–315
I. A. Panin, “The Equicharacteristic Case of the Gersten Conjecture”, Trudy Mat. Inst. Steklova, 241 (2003), 169–178; Proc. Steklov Inst. Math., 241 (2003), 154–163
I. A. Panin, A. L. Smirnov, “On a theorem of Grothendieck”, Zap. Nauchn. Sem. POMI, 272 (2000), 286–293; J. Math. Sci. (N. Y.), 116:1 (2003), 3042–3046
1998
27.
I. A. Panin, “Splitting principle and $K$-theory of simply connected semisimple algebraic groups”, Algebra i Analiz, 10:1 (1998), 88–131; St. Petersburg Math. J., 10:1 (1999), 68–101
I. A. Panin, A. A. Suslin, “On a conjecture of Grothendieck concerning Azumaya algebras”, Algebra i Analiz, 9:4 (1997), 215–223; St. Petersburg Math. J., 9:4 (1998), 851–858
I. A. Panin, “A splitting principle and the algebraic $K$-theory of some homogeneous varieties”, Zap. Nauchn. Sem. LOMI, 198 (1991), 49–64; J. Soviet Math., 64:1 (1993), 737–750
1989
30.
I. A. Panin, “Stabilization for orthogonal and symplectic algebraic $K$-theories”, Algebra i Analiz, 1:3 (1989), 172–195; Leningrad Math. J., 1:3 (1990), 741–764
I. A. Panin, “Algebraic $K$-theory of Grassmann varieties and their convoluted forms”, Funktsional. Anal. i Prilozhen., 23:2 (1989), 71–72; Funct. Anal. Appl., 23:2 (1989), 143–144
I. A. Panin, “Comparison of Quillen's and Volodin's $K$-theories”, Zap. Nauchn. Sem. LOMI, 175 (1989), 93–105; J. Soviet Math., 57:6 (1991), 3500–3507
1987
33.
I. A. Panin, “Homological stabilization for the symplectic and orthogonal groups”, Zap. Nauchn. Sem. LOMI, 160 (1987), 222–228
1986
34.
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; Math. USSR-Izv., 29:1 (1987), 119–131
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; J. Soviet Math., 26:3 (1984), 1901–1908
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; J. Soviet Math., 24:4 (1984), 449–452
F. A. Bogomolov, A. M. Vershik, S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarhin, S. V. Konyagin, Vik. S. Kulikov, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, I. A. Panin, V. P. Platonov, V. L. Popov, Yu. G. Prokhorov, A. L. Smirnov, “Alexey Nikolaevich Parshin (obituary)”, Uspekhi Mat. Nauk, 78:3(471) (2023), 165–169; Russian Math. Surveys, 78:3 (2023), 549–554
2022
38.
N. A. Vavilov, S. V. Vostokov, A. I. Generalov, N. L. Gordeev, E. V. Dybkova, I. M. Zilberbord, I. A. Panin, V. A. Petrov, K. I. Pimenov, A. A. Semjonov, A. L. Smirnov, A. V. Stepanov, “Anatoly Vladimirovich Yakovlev”, Zap. Nauchn. Sem. POMI, 513 (2022), 5–8
2020
39.
N. A. Vavilov, S. V. Vostokov, A. I. Generalov, N. L. Gordeev, E. V. Dybkova, I. M. Zilberbord, A. S. Merkurjev, I. A. Panin, V. A. Petrov, K. I. Pimenov, A. A. Semenov, A. L. Smirnov, A. V. Stepanov, “80 anniversary of Professor Anatolii Vladimirovich Yakovlev”, Zap. Nauchn. Sem. POMI, 492 (2020), 5–9
2018
40.
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; Russian Math. Surveys, 73:3 (2018), 519–531
2015
41.
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; St. Petersburg Math. J., 27:6 (2016), 861–862
2014
42.
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; Russian Math. Surveys, 69:4 (2014), 753–754
2000
43.
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; J. Math. Sci. (N. Y.), 116:1 (2003), 2883–2886
Presentations in Math-Net.Ru
1.
Главные расслоения. Семинар 4 I. A. Panin Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 27, 2024 11:15
2.
Главные расслоения. Семинар 3 I. A. Panin Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 24, 2024 15:30
3.
Главные расслоения. Семинар 2 I. A. Panin Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 22, 2024 11:15
4.
Главные расслоения. Семинар 1 I. A. Panin Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 21, 2024 11:15
5.
Лаборатория алгебры и теории чисел I. A. Panin Conference dedicated to the 90th anniversary of Steklov Mathematical Institute May 16, 2024 10:40
Вокруг стабильной мотивной гомотопической категории Воеводского I. A. Panin Conference “Geometry, topology and mathematical physics” on the occasion of the 85th anniversary of S.P. Novikov and the 80th anniversary of V.M. Buchstaber April 11, 2023 11:50
12.
Воспоминания об Алексее Николаевиче Паршине V. L. Popov, F. A. Bogomolov, B. S. Kashin, A. G. Sergeev, M. A. Korolev, S. O. Gorchinskiy, I. A. Panin “Numbers and functions” – Memorial conference for 80th birthday of Alexey Nikolaevich Parshin December 1, 2022 16:30
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
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