no. 2
Lower bounds for Betti numbers
Compositio Mathematica, Tome 86 (1993) no. 2, pp. 147-158. 
@article{CM_1993__86_2_147_0,
     author = {Avramov, Luchezar L. and Buchweitz, Ragnar-Olaf},
     title = {Lower bounds for {Betti} numbers},
     journal = {Compositio Mathematica},
     pages = {147--158},
     publisher = {Kluwer Academic Publishers},
     volume = {86},
     number = {2},
     year = {1993},
     mrnumber = {1214454},
     zbl = {0786.13004},
     language = {en},
     url = {http://www.numdam.org/item/CM_1993__86_2_147_0/}
}
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Avramov, Luchezar L.; Buchweitz, Ragnar-Olaf. Lower bounds for Betti numbers. Compositio Mathematica, Tome 86 (1993) no. 2, pp. 147-158. http://www.numdam.org/item/CM_1993__86_2_147_0/

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