Geodesic
Divisors on Varieties Over a Real Closed Field
Canadian mathematical bulletin, Tome 35 (1992) no. 4, pp. 503-509

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DOI

Let X be a projective nonsingular variety over a real closed field R such that the set X(R) of R-rational points of X is nonempty. Let ClR(X) = Cl(X)/Γ(X), where Cl(X) is the group of classes of linearly equivalent divisors on X and Γ(X) is the subgroup of Cl(X) consisting of the classes of divisors whose restriction to some neighborhood of X(R) in X is linearly equivalent to 0. It is proved that the group ClR(X) is isomorphic to (Z/2)s for some non-negative integer s. Moreover, an upper bound on s is given in terms of the Z/2-dimension of the group cohomology modules of Gal(C/R), where , with values in the Néron-Severi group and the Picard variety of Xc = X xR C.
DOI : 10.4153/CMB-1992-066-3
Mots-clés : 14C20, 14P05 
Kucharz, W. Divisors on Varieties Over a Real Closed Field. Canadian mathematical bulletin, Tome 35 (1992) no. 4, pp. 503-509. doi: 10.4153/CMB-1992-066-3
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     title = {Divisors on {Varieties} {Over} a {Real} {Closed} {Field}},
     journal = {Canadian mathematical bulletin},
     pages = {503--509},
     year = {1992},
     volume = {35},
     number = {4},
     doi = {10.4153/CMB-1992-066-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1992-066-3/}
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