Professor Alexei Skorobogatov is interested in arithmetic geometry, that is, in geometric approaches to number theory. The fundamental problem is to understand how the structure of solutions of Diophantine equations in number fields reflects the topological structure of the underlying algebraic variety. Alexei is also interested in analytical number theory, algebraic geometry, algebraic groups and the geometric invariant theory.
Alexei Skorobogatov's personal webpage can be found at http://www.ma.ic.ac.uk/~anskor/
Skorobogatov A, Loughran D, Smeets A, Pseudo-split fibres and arithmetic surjectivity, Annales Scientifiques De L'école Normale Supérieure, ISSN:0012-9593
Orr M, Skorobogatov AN, 2018, Finiteness theorems for K3 surfaces and abelian varieties of CM type, Compositio Mathematica, Vol:154, ISSN:0010-437X, Pages:1571-1592
Creutz B, Viray B, Skorobogatov AN, 2018, Degree and the Brauer-Manin obstruction, Algebra & Number Theory, Vol:12, ISSN:1937-0652, Pages:2445-2470
Ieronymou E, Skorobogatov AN, 2017, Odd order Brauer-Manin obstruction on diagonal quartic surfaces (vol 270, pg 181, 2015), Advances in Mathematics, Vol:307, ISSN:0001-8708, Pages:1372-1377