Effective structure theorems for symplectic spaces via height

Details Effective structure theorems for symplectic spaces via height Effective structure theorems for symplectic spaces via height

2008-01-30

arxiv.org/abs/0801.4773v1

in "Quadratic forms -- algebra, arithmetic, and geometry" (R. Baeza, W.K. Chan, D.W. Hoffmann, and R. Schulze-Pillot, eds.), C

Mathematics

Number Theory

Scientific paper

Given a $2k$-dimensional symplectic space $(Z,F)$ in $N$ variables, $1 < 2k \leq N$, over a global field $K$, we prove the existence of a symplectic basis for $(Z,F)$ of bounded height. This can be viewed as a version of Siegel's lemma for a symplectic space. As corollaries of our main result, we prove the existence of a small-height decomposition of $(Z,F)$ into hyperbolic planes, as well as the existence of two generating flags of totally isotropic subspaces. These present analogues of known results for quadratic spaces. A distinctive feature of our argument is that it works simultaneously for essentially any field with a product formula, algebraically closed or not. In fact, we prove an even more general version of these statements, where canonical height is replaced with twisted height. All bounds on height are explicit.

Affiliated with

Also associated with

No associations

Rating

Effective structure theorems for symplectic spaces via height 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 Effective structure theorems for symplectic spaces via height, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Effective structure theorems for symplectic spaces via height will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-203788