Reducibility mod p of hypersurfaces in projective spaces -: An application of arithmetic Bezout

[摘要] Given an absolutely irreducible horizontal hypersurface Z in a projective space over the ring of integers R of a number field, we give an explicit bound for the product of the norms of the prime ideals of R over which the fibre of Z becomes reducible. This bound is given as a function of a projective height of Z and is obtained using arithmetic intersection theory, in particular, an arithmetic Bezout theorem. (C) 2000 Academic Press.

[发布日期] 2000-10-01

[关键词] reducibility module p;hypersurfaces in P-s;arithmetic Bezout theorem;arithmetic intersection theory