Arithmetic E_8 lattices with maximal Galois action

Details Arithmetic E_8 lattices with maximal Galois action Arithmetic E_8 lattices with maximal Galois action

2008-03-20

arxiv.org/abs/0803.3063v1

LMS Journal of Computation and Mathematics 12 (2009) 144-165.

Mathematics

Number Theory

Latex, 21 pages. Magma scripts included at the end of the source file

Scientific paper

We construct explicit examples of E_8 lattices occurring in arithmetic for which the natural Galois action is equal to the full group of automorphisms of the lattice, i.e., the Weyl group of E_8. In particular, we give explicit elliptic curves over Q(t) whose Mordell-Weil lattices are isomorphic to E_8 and have maximal Galois action. Our main objects of study are del Pezzo surfaces of degree 1 over number fields. The geometric Picard group, considered as a lattice via the negative of the intersection pairing, contains a sublattice isomorphic to E_8. We construct examples of such surfaces for which the action of Galois on the geometric Picard group is maximal.

Affiliated with

Also associated with

No associations

Rating

Arithmetic E_8 lattices with maximal Galois action does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Arithmetic E_8 lattices with maximal Galois action, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arithmetic E_8 lattices with maximal Galois action will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-578411