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ON THE GROUP OF SEPARABLE QUADRATIC ALGEBRAS AND STACKS

Published online by Cambridge University Press:  20 June 2018

ILIA PIRASHVILI
ILIA PIRASHVILI*
Affiliation:
Institut für Mathematik, Universität Osnabrück, Albrechtstr. 28a, 49076 Osnabrück, Germany e-mails: ilia.pirashvili@uni-osnabrueck.de, ilia_p@ymail.com
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Abstract

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The aim of this paper is to study the group of isomorphism classes of torsors of finite flat group schemes of rank 2 over a commutative ring R. This, in particular, generalizes the group of quadratic algebras (free or projective), which is especially well studied. Our approach, however, yields new results even in this case.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 151 - 167
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

1. Bass, H., Algebraic K-theory (Benjamin, N. Y, 1968).Google Scholar
2. Bass, H., Lectures on topics in algebraic K-theory (Tata Institute of Fundamental Research, Bombay, 1967).Google Scholar
3. Gabriel, P. and Zisman, M., Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35 (Springer Verlag, Berlin, 1967).Google Scholar
4. Hahn, A. J., Quadratic algebras, Clifford algebras, and arithmetic Witt groups, Universitext (Springer Verlag, Berlin, 1993).Google Scholar
5. Kreimer, H. F., Quadratic Hopf algebras and Galois extensions, in Algebrasts' homage: Papers in ring theory and and related topics, Comtemp. Math. 13(1982), 353–361.Google Scholar
6. Moerdijk, I., Introduction to the language of stacks and gerbes. arXiv: math.AT/0212266.Google Scholar
7. Small, C., The group of quadratic extensions, J. Pure Appl. Algebra 2(1972), 83–105.Google Scholar
8. Vitale, E. M., A Picard-Brauer exact sequence of categorical groups, J. Pure Appl. Algebra 175(2002), 283–408.Google Scholar