Mesablishvili Bachuki

Full Name
Mesablishvili Bachuki
Address
: M. ALEXIDZE st.1 TBILISI 0193, GEORGIA
Phone
995 93 18 64 95
Fax
E-mail
Web Page
http://rmi.acnet.ge/~bachi
Date Of Birth
0000-00-00
Education
Tbilisi State university, 1998, Candidate of Phys. and Math. Sciences A.Razmadze Math. Inst., 1885–1989, Post graduate studies. Tbilisi state university, 1985, Graduated
Position
RAZMADZE MATHEMATICAL INSTITUTE, SENIOR RESEARCH FELLOW
Publications
1. The lattice of separable subalgebras of a radical extension of a connected ring. Bull. Georgian Acad. Sci., 126 (1987), pp.29-32. 2. Finite Galois extensions of a connected ring in an elementary topos. Bull. Georgian Acad. Sci. 135 (1989), pp. 32-36. 3. Fundamental theorem for finite Galois extensions of an internal commutative connected ring in an elementary topos and the functor T. Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 36 (1990), pp. 9-27. 4. Galois objects in the category of internal commutative algebras in an elementary topos and their flatness. Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 36 (1990), pp. 28-44. 5. Galois theory in a category of modulus over an elementary topos. Bull. Georgian Acad. Sci. 159 (1999), pp. 20-22 6. Pure morphisms of commuatative rings are effective descent morphisms for modules-a new proof. Theory Appl. Categ. 7 (2000), pp. 38-42. 7. (Effective) descent morphisms in the category of schemes. CT 2000, International summer conference in category theory, Como, Italy, pp.154- 156. 8. On some properties of pure morphisms of commuatative rings. Theory Appl. Categ. 10 (2002), pp.180-186 9. Descent theory for schemes. Appl. Categ. Structures 12 (2004), pp. 485-512. 10. Every small SL-enriched category is Morita equivalent to an SL-monoid . Theory Appl. Categ. 13 (2004), pp.169-171. 11. More on Descent theory for schemes. Georgian Mathematical Journal 11(4) (2004) , pp. 783-800. 12. Descent in categories of (co)algebras. Homology, Homotopy and Applications 7(1) (2005), pp. 1-8. 13. Monads of effective descent type and comonadicity, Theory and Applications of Categories, 16 (2006), pp. 1-45. 14. On the comonadicity of extension-of-scalars functors, arXiv: math. QA/0510272 (accepted for publication in Journal of Algebra). 15. On a generalization of Grothendieck’s theorem, arXiv: math.RA/0605470, 2006, Communications in Algebra (to appear). 16.Descent in *-autonomous categories, Journal of Pure and Applied Algebra (submitted).
Conferences,contacts,other scientific and educational activities
1. International Conference “Homological and Homotopical Algebra”, Tbilisi, Georgia 2000. 2. International summer conference in category theory “ CT 2000”, Como, Italy, 2000. 3. Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, The Fields Institute, Toronto, Canada, 2002. 4. Category Theory meeting, Haute-Bodeux, 7 to 13 September 2003, Belgium.
Participation in Grant Projects
1. INTAS-97-31961. 2. Fonds speciaux de recherché- FSR 2001, Belguim
Languages
Russian, English.
Scientific interests
Category Theory
Current scientific activities
Future work plans
CORING THEORY
Department
Theoretical Foundations in Mathematics