Pavel Sechin  Homepage
Pavel Sechin

I am a postdoc in the group of Marc Levine.
Research interests: cohomology theories of algebraic varieties
Email address: pavel.sechin@unidue.de
Curriculum vitae

Publications
 On the Structure of Algebraic Cobordism DOI [arXiv]
We investigate the structure of algebraic cobordism of LevineMorel as a module over the Lazard ring with the action of LandweberNovikov 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 Ktheory together with a topological filtration.
Advances in Mathematics, Volume 333, 31 July 2018, Pages 314–349

Chern Classes from Algebraic Morava Ktheories to Chow Groups DOI
[arXiv]
We calculate the ring of unstable (possibly nonadditive) operations from Morava Ktheory
to Chow groups with plocal coefficients.
More precisely, we prove that it is a formal power series ring on generators which satisfy a Cartantype formula.
International Mathematics Research Notice, available online: March 2017, printed: August 2018, Vol. 2018, No. 15, pp. 4675–4721
 The Category of Flat Hodge–Tate Structures DOI
We describe the full subcategory
of the category of HodgeTate structures on which
the (essentially unique) arithmetic GaussManin connection (constructed by M. Rovinsky) is flat.
Mathematical Notes, 2016
Preprints
 Chern classes from Morava Ktheories to p^{n}typical oriented theories [arXiv]
We generalize the notion of ptypical formal group laws to p^{n}typical and study operations
from nth Morava Ktheory K(n) to an arbitrary p^{n}typical oriented theory.
If the ring of coefficients of the p^{n}typical theory is torsionfree,
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 Ktheories.
 Applications of the Morava Ktheory to algebraic groups (joint with Nikita Semenov)
[arXiv]
We study relations between vanishing of cohomological invariants of algebraic groups and splitting of Morava Ktheory motives.
For quadrics the nth Morava Ktheory detects vanishing of all invariants of degree less than n+2.
The second Morava Ktheory detects vanishing of Rost invariants, the fourth Morava Ktheory detects splitting of groups of type E_{8}.
We provide new estimates on torsion in codimensions up to 2^{n} 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 Ktheories to p^{n}typical oriented theories
 SanktPetersburg, Chebyshev Laboratory November 2016
 Moscow, HSE, Workshop "Motives, Periods and Lfunctions" April 2017
 Munich, LMU June 2017
 SanktPetersburg, Summer School "Motives and related structures" September 2018
 Chern classes from Morava Ktheory to Chow groups
 Oberwolfach, MFO, Workshop "Algebraic Cobordism and Projective Homogeneous Varieties" February 2016
 Munich, LMU May 2016
Past and future events
 Augsburg, F1Geometry and Motives, Nov. 89, 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 213, 2019
 Darmstadt, Technische Universität, MiniWorkshop on Infinity Categories, February 1415, 2019
 St. Peterburg, Euler International Mathematical Institute, Motives in St. Petersburg, September 314, 2018
 Essen, Universität DuisburgEssen, "Motivic homotopy theory and refined enumerative geometry", May 1418, 2018
 Freiburg, FRIAS, Winter School: A1Homotopy Theory, February 2018
 Heidelberg, RuprechtKarlsUniversität, "Étale and motivic homotopy theory", September 2017
 Munich, LMU, "Motives: arithmetic, algebraic geometry and topology under the whiteblue sky", July 2017
 Bonn, HCM, "KTheory and Related Fields", May 2017
 Oberwolfach, MFO, "Algebraic Cobordism and Projective Homogeneous Varieties", February 2016
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