Publications

Book

(with V.P. Platonov and A.S. Rapinchuk) Algebraic Groups and Number Theory, Vol. 1 of the Second Edition, Cambridge Studies Adv. Math. 205, Cambridge University Press, 2023 (publisher's website) 

Paper and Preprints

29. (with A.S. Rapinchuk) The finiteness of the Tate-Shafarevich group over  function fields for algebraic tori defined over the base field, to appear in Comptes Rendus --- Série Mathématique (arxiv) 

28. Residue maps, Azumaya algebras, and buildings, to appear in Journal of Pure & Applied Algebra (arxiv) 

27. (with P. Abramenko and A.S. Rapinchuk) Applications of the Fixed Point Theorem for group actions on buildings to algebraic groups over polynomial rings, to appear in Journal of Algebra (arxiv) 

26.  Algebraic groups with good reduction and the genus problem, to appear in the proceedings of the Amitsur Centennial Symposium (arxiv) 

25. (with V.I. Chernousov and A.S. Rapinchuk) Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction, Adv. Math. 438 (2024), Paper No. 109437, 78 pp (arxiv) 

24. (with J. Ruiter) On abstract homomorphisms of some special unitary groups, to appear in Proc. Amer. Math. Soc.  150 (2022), no. 10, 4241-4258 (arxiv) 

23. (with A.S. Rapinchuk) Finiteness theorems for algebraic tori over function fields, C. R. Math. Acad. Sci. Paris 359 (2021), 939–944.  (pdf) 

22. (with A.S. Rapinchuk) Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties, Math. Res. Lett. 30 (2023), No. 3, 913-943 (arxiv) 

21. (with A.S. Rapinchuk) Recent developments in the theory of linear algebraic groups: Good reduction and finiteness properties, Notices Amer. Math. Soc.  68 (2021), no. 6, 899–910. (journal version)   (arxiv)  

20. (with A.S. Rapinchuk) Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields, J. Number Theory 233(2022), 228-260. (arxiv) 

19. (with A.S. Rapinchuk) Linear algebraic groups with good reduction, Res. Math. Sci. 7 (2020), no. 3, Paper No. 28 (arxiv)

18. (with V.I. Chernousov and A.S. Rapinchuk) The finiteness of the genus of a finite-dimensional division algebra, and generalizations, Israel J. Math. 236 (2020), no. 2, 747-799 (arxiv)

17. (with V.I. Chernousov and A.S. Rapinchuk) Spinor groups with good reduction, Compositio Math. 155 (2019), no. 3, 484-527  (arxiv)

16. On residue maps for affine curves, J. Pure Appl. Algebra 223 (2019), no. 3, 965-975 (arxiv)

15. On abstract homomorphisms of Chevalley groups over the coordinate rings of affine curves, Transformation Groups 24 (2019), no. 4, 1241-1259 (arxiv)

14. A generalization of Serre's condition (F) with applications to the finiteness of unramified cohomology, Math. Z. 291 (2019), no. 1-2, 199-213 (arxiv)

13. (with V.I. Chernousov and A.S. Rapinchuk) On some finiteness properties of algebraic groups over finitely generated fields, C. R. Acad. Sci. Paris, Ser. I 354 (2016), 869-873 (pdf)

12. (with M. Boyarchenko) On abstract representations of the groups of rational points of algebraic groups in positive characteristic, Arch. Math. (Basel) 107 (2016), no. 6, 569-580. (arxiv)

11. (with V.I. Chernousov and A.S. Rapinchuk) On the size of the genus of a division algebra, Trudy MIAN 292 (2016) (arxiv)

10. (with V.I. Chernousov and A.S. Rapinchuk) Division algebras with the same maximal subfields, Russian Math. Surveys 70(1) (2015), 83-112. (arxiv)

9. On the character varieties of finitely generated groups, Math. Res. Lett. 22(2) (2015), 579-604. (arxiv)

8. On the conjecture of Borel and Tits for abstract homomorphisms of algebraic groups, Oberwolfach Report 17/2013, 1061-1063

7. Abstract homomorphisms of algebraic groups and applications, in the proceedings of the Conference on Group Actions and Applications in Geometry, Topology, and Analysis, Kunming, July 2012 (pdf)

6. (with V.I. Chernousov and A.S. Rapinchuk) The genus of a division algebra and the unramified Brauer group, Bull. Math. Sci. 3 (2013), 211-240. (arxiv)

5. (with V.I. Chernousov and A.S. Rapinchuk) On the genus of a division algebra, C. R. Acad. Sci. Paris, Ser. I 350, 807-812 (2012) (pdf)

4. On abstract representations of the groups of rational points of algebraic groups and their deformations, Algebra and Number Theory 7 (7) (2013), 1685-1723. (pdf)

3. (with A.S. Rapinchuk) Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank > 1 over noetherian rings, Proc. Amer. Math. Soc. 139, no. 9, 3099-3113 (2011) (arxiv)

2. On linear representations of Chevalley groups over commutative rings, Proc. Lond. Math. Soc. (3) 102, no. 5, 951-983 (2011) (arxiv)

1. (with A.S. Rapinchuk) On division algebras having the same maximal sub.fields, Manuscripta Math. 132, no. 3-4, 273-293 (2010) (arxiv)