Pavel Sechin - Homepage
I am a postdoc in the group of Marc Levine.
Research interests: cohomology theories of algebraic varieties
Email address: email@example.com
- On the Structure of Algebraic Cobordism DOI [arXiv]
Advances in Mathematics, Volume 333, 31 July 2018, Pages 314–349
We investigate the structure of algebraic cobordism of Levine-Morel as a module over the Lazard ring with the action of Landweber-Novikov and symmetric operations on it.
We also prove the Syzygies Conjecture of Vishik on the existence of certain free resolutions of algebraic cobordism,
and show that algebraic cobordism of a smooth surface can be described in terms of K-theory together with a topological filtration.
Chern Classes from Algebraic Morava K-theories to Chow Groups DOI
International Mathematics Research Notice, available online: March 2017, printed: August 2018, Vol. 2018, No. 15, pp. 4675–4721
We calculate the ring of unstable (possibly nonadditive) operations from Morava K-theory
to Chow groups with p-local coefficients.
More precisely, we prove that it is a formal power series ring on generators which satisfy a Cartan-type formula.
- The Category of Flat Hodge–Tate Structures DOI
We describe the full subcategory
of the category of Hodge-Tate structures on which
the (essentially unique) arithmetic Gauss-Manin connection (constructed by M. Rovinsky) is flat.
Mathematical Notes, 2016
- Chern classes from Morava K-theories to pn-typical oriented theories [arXiv]
We generalize the notion of p-typical formal group laws to pn-typical and study operations
from n-th Morava K-theory K(n) to an arbitrary pn-typical oriented theory.
If the ring of coefficients of the pn-typical theory is torsion-free,
we show that all operations from K(n) are generated by 'Chern classes'.
In particular, this allows us to introduce the gamma filtration on Morava K-theories.
- Applications of the Morava K-theory to algebraic groups (joint with Nikita Semenov)
We study relations between vanishing of cohomological invariants of algebraic groups and splitting of Morava K-theory motives.
For quadrics the n-th Morava K-theory detects vanishing of all invariants of degree less than n+2.
The second Morava K-theory detects vanishing of Rost invariants, the fourth Morava K-theory detects splitting of groups of type E8.
We provide new estimates on torsion in codimensions up to 2n of quadrics as above as well as provide a general method for estimation.
Selected conference and seminar talks
- On the Structure of Algebraic Cobordism
- Heidelberg, Mathematishes Institut May 2018
- Munich, LMU July 2019
- Chern classes from Morava K-theories to pn-typical oriented theories
- Sankt-Petersburg, Chebyshev Laboratory November 2016
- Moscow, HSE, Workshop "Motives, Periods and L-functions" April 2017
- Munich, LMU June 2017
- Sankt-Petersburg, Summer School "Motives and related structures" September 2018
- Chern classes from Morava K-theory to Chow groups
- Oberwolfach, MFO, Workshop "Algebraic Cobordism and Projective Homogeneous Varieties" February 2016
- Munich, LMU May 2016
Past and future events
↑ Back to the start
- Augsburg, F1-Geometry and Motives, Nov. 8-9, 2019
- Essen, 2nd “Jahrestagung” of the DFG Priority Program 1786 “Homotopy theory and algebraic geometry”, Sept. 30 - Oct. 2, 2019
- St. Peterburg, Euler International Mathematical Institute, Algebraic Groups and Motives, September 2-13, 2019
- Darmstadt, Technische Universität, Mini-Workshop on Infinity Categories, February 14-15, 2019
- St. Peterburg, Euler International Mathematical Institute, Motives in St. Petersburg, September 3-14, 2018
- Essen, Universität Duisburg-Essen, "Motivic homotopy theory and refined enumerative geometry", May 14-18, 2018
- Freiburg, FRIAS, Winter School: A1-Homotopy Theory, February 2018
- Heidelberg, Ruprecht-Karls-Universität, "Étale and motivic homotopy theory", September 2017
- Munich, LMU, "Motives: arithmetic, algebraic geometry and topology under the white-blue sky", July 2017
- Bonn, HCM, "K-Theory and Related Fields", May 2017
- Oberwolfach, MFO, "Algebraic Cobordism and Projective Homogeneous Varieties", February 2016