Galois representations, Mumford-Tate groups and good reduction of abelian varieties

Details Galois representations, Mumford-Tate groups and good reduction of abelian varieties Galois representations, Mumford-Tate groups and good reduction of abelian varieties

2003-02-11

arxiv.org/abs/math/0302117v2

Math. Ann. 329, 119-160 (2004)

Mathematics

Number Theory

Minor modifications and corrections

Scientific paper

Let K be a number field and A an abelian variety over K. We are interested in the following conjecture of Morita: if the Mumford-Tate group of A does not contain unipotent Q-rational points then A has potentially good reduction at any discrete place of K. The Mumford-Tate group is an object of analytical nature whereas having good reduction is an arithmetical notion, linked to the ramification of Galois representations. This conjecture has been proved by Morita for particular abelian varieties with many endomorphisms (called of PEL type). Noot obtained results for abelian varieties without non trivial endomorphisms (Mumford's example, not of PEL type). We give new results for abelian varieties not of PEL type.

Affiliated with

Also associated with

No associations

Rating

Galois representations, Mumford-Tate groups and good reduction of abelian varieties 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 Galois representations, Mumford-Tate groups and good reduction of abelian varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Galois representations, Mumford-Tate groups and good reduction of abelian varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-410361