✦ LIBER ✦
Reducibility mod p of Hypersurfaces in Projective Spaces—An Application of Arithmetic Bézout
✍ Scribed by Reinie Erné
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 160 KB
- Volume
- 84
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
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 Be zout theorem.