Geodesic
ON HOMOLOGICAL FROBENIUS COMPLEXES AND BIMODULES
Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 629-642

Voir la notice de l'article provenant de la source Cambridge University Press

We introduce the concept of homological Frobenius functors as the natural generalization of Frobenius functors in the setting of triangulated categories, and study their structure in the particular case of the derived categories of those of complexes and modules over a unital associative ring. Tilting complexes (modules) are examples of homological Frobenius complexes (modules). Homological Frobenius functors retain some of the nice properties of Frobenius ones as the ascent theorem for Gorenstein categories. It is shown that homological Frobenius ring homomorphisms are always Frobenius.
DOI : 10.1017/S0017089514000068
Mots-clés : Primary 16E65, Secondary 18E30 
ROZAS, J. R. GARCÍA; OYONARTE, LUIS; TORRECILLAS, BLAS. ON HOMOLOGICAL FROBENIUS COMPLEXES AND BIMODULES. Glasgow mathematical journal, Tome 56 (2014) no. 3, pp. 629-642. doi: 10.1017/S0017089514000068
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[1] 1.Abe, H. and Hoshino, M., Frobenius extensions and tilting complexes, Alg. Rep. Theory 11 (2008), 215–232. Google Scholar

[2] 2.Caenepeel, S., Militaru, G. and Zhu, S., Frobenius and seperable functors for generalized module categories and nonlinear equations, Lecture Notes in Mathematics, vol. 1787 (Springer, Berlin, Germany, 2002). Google Scholar

[3] 3.Castaño Iglesias, F., Torrecillas, J. Gómez and Nastasescu, C., Frobenius functors: Applications, Comm. Algebra 27 (10) (1999), 4879–4900. Google Scholar

[4] 4.Chen, X.-W., Totally reflexive extensions and modules, J. Algebra 379 (1) (2013) 322–332. Google Scholar

[5] 5.Chen, H. and Xi, C., Homological ring epimorphisms and recollements from exact pairs, I. arXiv:1203.5168 (preprint). Google Scholar

[6] 6.Enochs, E., Estrada, S. and García Rozas, J. R., Gorenstein categories and Tate cohomology on projective schemes, Math. Nachr. 281 (4) (2008), 525–540. Google Scholar

[7] 7.Enochs, E., Herzog, I. and Park, S., Cyclic quiver rings and polycyclic-by-finite group rings, Houston J. Math. 25 (1) (1999), 113. Google Scholar

[8] 8.Enochs, E. and Jenda, O., Relative homological algebra, vol. 2, De Gruyter Expositions in Mathematics, vol. 54 (De Gruyter, Berlin, Germany, 2011). Google Scholar

[9] 9.Hoshino, M. and Kato, Y., Tilting complexes defined by idempotents, Comm. Algebra 30 (1) (2002), 83–100. Google Scholar

[10] 10.Kadison, L., New examples of Frobenius extensions, University Lecture Series, 14 (American Mathematical Society, Providence, RI, 1999). Google Scholar

[11] 11.Kadison, L., Separability and the twisted Frobenius bimodule, Alg. Rep. Theory 2 (1999), 397–414. Google Scholar

[12] 12.Krause, H., Smashing subcategories and the telescope conjecture – an algebraic approach, Invent. Math. 139 (1) (2000), 99–133. Google Scholar

[13] 13.Minamoto, H. and Mori, I., The structure of AS-Gorenstein algebras, Adv. Math. 226 (5) (2011), 4061–4095. Google Scholar

[14] 14.Miyachi, J., Derived categories with applications to representation of algebras. Personal notes. Available at http://www.u-gakugei.ac.jp/~miyachi/papers/ChibaSemi.pdf, accessed 2 May 2012. Google Scholar

[15] 15.Morita, K., Adjoint pairs of functors and Frobenius extensions, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A, 9 (1965), 40–71. Google Scholar

[16] 16.Neeman, A., The Grothendieck duality theorem via Bousfields techniques and Brown representability, J. Amer. Math. Soc. 9 (1996), 205–236. Google Scholar

[17] 17.Neeman, A., Triangulated categories, Annals of Mathematics Studies, vol. 148 (Princeton University Press, Princeton, NJ, 2001). Google Scholar | DOI

[18] 18.Serpé, C., Resolution of unbounded complexes in Grothendieck categories, J. Pure Appl. Algebra, 177 (2003), 103–112. Google Scholar

[19] 19.Spaltenstein, N., Resolutions of unbounded complexes, Compositio Math. 65 (1988), 121–154. Google Scholar

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