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You are here: FRIAS Fellows and Alumni Fellows Prof. Dr. Alexei Skorobogatov

Prof. Dr. Alexei Skorobogatov

Imperial College London
Mathematics

External Senior Fellow (Marie S. Curie FCFP)
September 2021 - December 2021

Room 02 009
Phone +49 (0)761 - 203 97318

CV

I received PhD in mathematics from Moscow State University in 1987, where I was supervised by Yuri Manin. I worked at the Institute for the Information Transmission Problems, Russian Academy of Sciences, and at the Institut Mathématique de Luminy, CNRS (Marseille). In 1997, I was a visiting researcher at the Max-Planck-Institut für Mathematik in Bonn. From 1998 I work as Lecturer, Reader, and then Professor (2003) at Imperial College London. My research is in arithmetic and algebraic geometry, motivated by applications to rational points and Diophantine equations, with focus on the Brauer group and the Brauer-Manin obstruction. I published over 75 research papers and two books (the most recent one, “The Brauer-Grothendieck group” is co-authored with J.-L. Colliot-Thélène and will be published by Springer this year), and co-edited two collections of papers. I received the Whitehead prize of the London Mathematical Society in 2001.

Selected Publications

  • On the decoding of algebraic-geometric codes. IEEE Trans. Inform. Theory 36 (1990) 1051--1060. (with S. G. Vladut)
  • Hasse principle for pencils of curves of genus one whose Jacobians have rational 2-division points. Inv. Math.  134 (1998) 579--650. (with J.-L. Colliot-Thélène and Sir Peter Swinnerton-Dyer)
  • Beyond the Manin obstruction. Inv. Math. 135 (1999) 399-424.
  • Rational points on pencils of conics and quadrics with many degenerate fibres. Ann. of Math. 180 (2014) 381-402 (with T. Browning and L. Matthiesen)
  • Finiteness theorems for K3 surfaces and abelian varieties of CM type. Compositio Math. 154 (2018) 1571-1592. (with M. Orr)

FRIAS Research Project

p-adic methods in the Brauer--Manin obstruction

The area of the proposed research is a modern development of Diophantine equations, a classical area of number theory. This subject belongs to arithmetic and algebraic geometry, and concerns rational points of algebraic varieties over local and global fields, the Brauer group and the Brauer--Manin obstruction. I would like to investigate new p-adic methods that apply fundamental results of K. Kato to the evaluation of elements of the Brauer group at local points when the torsion of a Brauer element is divisible by the residual characteristic. These methods have applications to the computation of the Brauer--Manin set. One concrete situation is that of diagonal surfaces in the projective space, where some work in this direction has already been done. This is related to the current research on open problems concerning rational points and reduction of K3 surfaces.