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Ring of operations from Morava K-theories to Chow groups
Mathematical notes. 2017. Vol. 101. No. 1. P. 176–180.
Sechin P.
Sechin P., Semenov N., Annales Scientifiques de l'Ecole Normale Superieure 2021 Vol. 54 No. 4 P. 945–990
In this article we discuss an approach to cohomological invariants of algebraic groups based on the Morava K-theories.
We show that the second Morava K-theory detects the triviality of the Rost invariant and, more generally, relate the triviality of cohomological invariants and the splitting of Morava motives.
We compute the Morava K-theory of generalized Rost motives and of some affine ...
Added: October 28, 2021
Sechin P., / Series arXiv "math". 2018.
Generalizing the definition of Cartier, we introduce pn-typical formal group laws over ℤ(p)-algebras. An oriented cohomology theory in the sense of Levin-Morel is called pn-typical if its corresponding formal group law is p^n-typical. The main result of the paper is the construction of 'Chern classes' from the algebraic n-th Morava K-theory to every p^n-typical oriented cohomology theory.
If the coefficient ring of ...
Added: December 6, 2018
Sechin P., Semenov N., / Series arXiv "math". 2018.
In the present article we discuss an approach to cohomological invariants of algebraic groups over fields of characteristic zero based on the Morava K-theories, which are generalized oriented cohomology theories in the sense of Levine--Morel.
We show that the second Morava K-theory detects the triviality of the Rost invariant and, more generally, relate the triviality of cohomological invariants ...
Added: December 6, 2018
Sechin P., International Mathematics Research Notices 2017 P. 1–24
In this article, we calculate the ring of unstable (possibly nonadditive) operations from algebraic Morava K-theory K(n)^∗ to Chow groups with ℤ_(p) -coefficients. More precisely, we prove that it is a formal power series ring on generators c_i:K(n)^∗→CH^i⊗ℤ_(p) , which satisfy a Cartan-type formula. ...
Added: March 25, 2017
Sechin P., Математические заметки 2017 Т. 101 № 1 С. 150–154
Мы вычисляем кольцо операций из алгебраических К-теорий Моравы в группы Чжоу с локализованными коэффициентами. ...
Added: September 8, 2016
Sechin P., / Series arXiv "math". 2016.
In this paper we calculate the ring of unstable (possibly non-additive) operations from algebraic Morava K-theory K(n) to Chow groups with ℤ(p)-coefficients. More precisely, we prove that it is a formal power series ring on generators c_i:K(n)→CH^i⊗ℤ(p), which satisfy a Cartan-type formula. ...
Added: May 18, 2016