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Abstract:

Strong similarities have been long observed between the Galois and Tannaka theories of the representation of groups. In this paper we construct an explicit (neutral) Tannakian context for the Galois theory of atomic topoi and prove equivalence for the fundamental theorem. Since the theorem is known for the Galois context, this yields a proof of the fundamental (recognition) theorem for a new Tannakian context. This example is different from the additive cases or their generalization for which the theorem is known to hold and for which the unit of the tensor product is always an object of finite presentation, which is not the case in our context. © 2012 Elsevier Ltd.

Registro:

Documento: Artículo
Título:A Tannakian context for Galois theory
Autor:Dubuc, E.J.; Szyld, M.
Filiación:University of Buenos Aires, F.C.E.y N., Departamento de Matemáticas, Buenos Aires, 1428 CABA, Argentina
Palabras clave:Atomic topos; Grothendieck-Galois; Locale-valued bijections; Tannaka
Año:2013
Volumen:234
Página de inicio:528
Página de fin:549
DOI: http://dx.doi.org/10.1016/j.aim.2012.10.018
Título revista:Advances in Mathematics
Título revista abreviado:Adv. Math.
ISSN:00018708
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00018708_v234_n_p528_Dubuc

Referencias:

  • Artin, M., Grothendieck, A., Verdier, J., SGA 4 (1963-64) (1972) Springer Lecture Notes in Mathematics, 269-270
  • Chikhladze, D., The Tannaka representation theorem for separable Frobenius functors (2010), arxiv:1008.1400v1; Dubuc, E.J., Localic Galois theory (2003) Adv. Math., 175, pp. 144-167
  • Grothendieck, A., SGA1 (1960-61) (1971) Springer Lecture Notes in Mathematics, 224
  • Ho Hai, P., Tannaka-Krein duality for Hopf algebroids (2008) Isr. J. Math., 167, pp. 193-225
  • Janelidze, G., Street, R., Galois theory in symmetric monoidal categories (1999) J. Algebra, 220, pp. 174-187
  • Joyal, A., Street, R., An introduction to Tannaka duality and quantum groups (1991) Lect. Notes Math., 1488, pp. 413-492
  • Joyal, A., Street, R., (1992), Braided tensor categories, Macquarie Mathematics Reports, Report No. 92-091; Joyal, A., Tierney, M., An extension of the Galois theory of Grothendieck (1984) Memoirs of the American Mathematical Society, 151
  • Pareigis, B., Reconstruction of hidden symmetries (1996) J. Algebra, 183, pp. 90-154
  • Rochard, X., (1997), http://www.math.jussieu.fr/maltsin/, Théorie Tannakienne nonadditive, Doctoral Thesis, Université Paris 7, Avalailable at ; Schappi, D., Tannaka duality for comonoids in cosmoi (2011), arxiv:1112.5213v1; Schauenburg, P., Tannaka duality for arbitrary Hopf algebras (1992) Algebra Berichte, 66. , Verlag Reinhard Fischer, Munich
  • Szyld, M., (2009), arxiv:1110.5293v1, On Tannaka duality, Tesis de Licenciatura, Universidad de Buenos Aires, , 2011; Wraith, G., Localic groups (1981) Cah. Topol. Géom. Différ. Catég., 22, pp. 61-66

Citas:

---------- APA ----------
Dubuc, E.J. & Szyld, M. (2013) . A Tannakian context for Galois theory. Advances in Mathematics, 234, 528-549.
http://dx.doi.org/10.1016/j.aim.2012.10.018
---------- CHICAGO ----------
Dubuc, E.J., Szyld, M. "A Tannakian context for Galois theory" . Advances in Mathematics 234 (2013) : 528-549.
http://dx.doi.org/10.1016/j.aim.2012.10.018
---------- MLA ----------
Dubuc, E.J., Szyld, M. "A Tannakian context for Galois theory" . Advances in Mathematics, vol. 234, 2013, pp. 528-549.
http://dx.doi.org/10.1016/j.aim.2012.10.018
---------- VANCOUVER ----------
Dubuc, E.J., Szyld, M. A Tannakian context for Galois theory. Adv. Math. 2013;234:528-549.
http://dx.doi.org/10.1016/j.aim.2012.10.018