Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: Website: https://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.
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.
