Geodesic
Birational invariants for the torus without affect in a~group of $F_4$ type
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2009), pp. 57-68

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In the paper all the cohomological birational invariants for the torus without affect in a semisimple exceptional group of $F_4$ type are calculated. Kunyavski B. and Cortella A. have proved that this torus is not rational. We prove that the Picard group of a projective model for the studied torus is not cohomologically trivial. We find all the subgroups in Weyl group $W(F_4)$ for which the corresponding cohomological invariant is not trivial.
Mots-clés : algebraic torus, birational invariant
Keywords: cohomology, flasque resolution, semisimple group. 
@article{VSGU_2009_6_a5,
     author = {Yu. Yu. Krutikov},
     title = {Birational invariants for the torus without affect in a~group of $F_4$ type},
     journal = {Vestnik Samarskogo universiteta. Estestvennonau\v{c}na\^a seri\^a},
     pages = {57--68},
     publisher = {mathdoc},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGU_2009_6_a5/}
}
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Yu. Yu. Krutikov. Birational invariants for the torus without affect in a~group of $F_4$ type. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 6 (2009), pp. 57-68. http://geodesic.mathdoc.fr/item/VSGU_2009_6_a5/