A fano variety is a smooth, geometrically connected variety over a field, for which the dualizing sheaf is anti-ample. For example the projective space, more generally flag varieties are Fano varieties, as well as hypersurfaces of degree d ≤ 𝑛 in ℙ𝑛. We discuss the existence and number of rational points over a finite field, the Hodge type over the complex numbers, and the motivic conjectures which are controlling those invariants. We present a geometric version of it.
@article{1675,
title = {Congruences for the Number of Rational Points, Hodge Type and Motivic Conjectures for Fano Varieties},
journal = {CUBO, A Mathematical Journal},
volume = {5},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/1675}
}
Bloch, Spencer; Esnault, Helene. Congruences for the Number of Rational Points, Hodge Type and Motivic Conjectures for Fano Varieties. CUBO, A Mathematical Journal, Tome 5 (2003) . http://gdmltest.u-ga.fr/item/1675/