Pavel Sechin

Publications

• Morava J-invariant (joint with Nikita Geldhauser, Andrei Lavrenov and Victor Petrov) DOI [arXiv]
  We compute the co-multiplication of the algebraic Morava K-theory for split orthogonal groups. This allows us to compute the decomposition of the Morava motives of generic maximal orthogonal Grassmannians and to compute a Morava K-theory analogue of the J-invariant in terms of the ordinary (Chow) J-invariant.
  Forum of Mathematics, Sigma, Volume 13, 2025
• Morava K-theory of orthogonal groups and motives of projective quadrics (j.w. Nikita Geldhauser, Andrei Lavrenov and Victor Petrov) DOI [arXiv] We compute the algebraic Morava K-theory ring for all split orthogonal groups.
  As an application we describe the Morava motive of a generic quadric and of its maximal orthogonal Grassmannian.
  Advances in Mathematics, Volume 446, June 2024, 109657
• Applications of the Morava K-theory to algebraic groups (joint with Nikita Geldhauser) 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, 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

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Preprints

• Invertible Morava motives in quadrics [arXiv] (joint with Andrei Lavrenov)
  We construct invertible motives associated to elements in Milnor K-theory modulo 2 and investigate the Morava motives of quadrics.
  We conjecture that Morava motives yield a new approach to cohomological invariants.
• 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

• Cohomological invariants and invertible Morava motives
• PCMI 2024, research program seminar   July 2024

• 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

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Past and future events

• Paris, Quadratic forms and algebraic cycles (A conference in the honor of Nikita Karpenko), 29 - 31 October, 2025
• Dortmund, Squares in Dortmund (Detlev Hoffman's 64th birthday), 31 March - 4 April, 2025
• Park City, UT, USA, PCMI 2024 Research program, July 7-27, 2024
• 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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