Igor Rapinchuk

Assistant Professor 
Michigan State University
East Lansing, MI 48824                                                                                                                                                                                       

Office: D321 Wells Hall
Email: rapinchu AT msu DOT edu












Teaching, mentoring, and service


Research

I am broadly interested in algebra, algebraic number theory, and arithmetic geometry. Much of my current research deals with the arithmetic of algebraic groups over higher-dimensional fields and Galois cohomology. I also work on the analysis of abstract homomorphisms of algebraic groups over general fields and rings. Further details can be found in this research summary

Videos of my talks at the Banff International Research Station and the Institute for Advanced Study can be found hereherehere, and here.

Publications

19. (with A.S. Rapinchuk) Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields, preprint (arxiv) 

18. (with V.I. Chernousov and A.S. Rapinchuk) The finiteness of the genus of a finite-dimensional division algebra, and generalizations, to appear in Israel Journal of Mathematics (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 curvesJ. 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 algebraTrudy 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. (pdf)

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

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. (2013), 211-240. (pdf)

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) (pdf)

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

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


Expository papers

1. Dirichlet's prime number theorem: Algebraic and analytic aspects, The Harvard College Math Review 1, no. 1, 15-29 (2007) (pdf)

2. The Brauer group of a field (pdf)

3. A proof of the Kronecker-Weber Theorem (pdf)

4. On Bézout's theorem and some of its applications (pdf) 

5. Elliptic Curves with Complex Multiplication and Kronecker's Jugendtraum (pdf)

6. An arithmetic Riemann-Roch-Grothendieck theorem (pdf)