Glossary of Arithmetic and Diophantine Geometry - L

L

Linear torus

A linear torus is a geometrically irreducible Zariski-closed subgroup of an affine torus (product of multiplicative groups).

Local zeta-function

A local zeta-function is a generating function for the number of points on an algebraic variety V over a finite field F, over the finite field extensions of F. According to the Weil conjectures (q.v.) these functions, for non-singular varieties, exhibit properties closely analogous to the Riemann zeta-function, including the Riemann hypothesis.