Pavel Sechin

CV

Publications

Preprints

Talks

Events

Oberseminar on Grothendieck ring of varieties and birationa geometry

Publications

• Applications of the Morava K-theory to algebraic groups (joint with Nikita Semenov) DOI [arXiv]
      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.
Annales scientifiques de l'ENS, Tome 54, Fascicule 4, Pages 945-990, 2021
• On the Structure of Algebraic Cobordism DOI [arXiv]
      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.
   Advances in Mathematics, Volume 333, 31 July 2018, Pages 314–349
• Chern Classes from Algebraic Morava K-theories to Chow Groups DOI [arXiv]
      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.
   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 Hodge-Tate structures on which
      the (essentially unique) arithmetic Gauss-Manin connection (constructed by M. Rovinsky) is flat.
     Mathematical Notes, 2016

Preprints

• Morava K-theory of orthogonal groups and motives of projective quadrics (joint with Andrei Lavrenov, Victor Petrov and Nikita Semenov) [arXiv]
      We consider the category of (pure) Morava K-theory motives. For a generic quadric Q we determine all indecomposable summands of the Morava motive of Q. Besides, we compute the algebraic Morava K-theory ring for all split orthogonal groups. Finally, we provide criteria when motivic decompositions of projective homogeneous varieties for Morava K-theory motives with Fp-coefficients can be lifted to motivic decomposition of Z_(p)-integral Morava motives.
• 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.

Selected conference and seminar talks

• Morava motive of an element in Milnor K-theory modulo 2
• Essen, "Harnessing motivic invariants"   June 2022

• On the Structure of Algebraic Cobordism
• Heidelberg, Mathematishes Institut   May 2018
• Munich, LMU   July 2019
• St. Petersburg, Euler Institute, "Emerging research in algebraic groups, motives and K-theory"   September 2019
• Applications of Morava K-theories to algebraic groups
• Essen, DEU, 2nd Jahrestagung of SPP 1786   October 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

• Augsburg, Algebraic Geometry Day in Augsburg, 13 January 2023
• Regensburg, Summer school "Motives in Ratisbona", Sep. 12-16, 2022
• Essen, Harnessing motivic invariants, June 27-July 1, 2022
• 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

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