Gauss composition over an arbitrary base

Details Gauss composition over an arbitrary base Gauss composition over an arbitrary base

2010-07-29

arxiv.org/abs/1007.5285v1

Adv. Math., 226 (2011) 1756-1771

Mathematics

Number Theory

submitted

Scientific paper

10.1016/j.aim.2010.08.018

The classical theorems relating integral binary quadratic forms and ideal classes of quadratic orders have been of tremendous importance in mathematics, and many authors have given extensions of these theorems to rings other than the integers. However, such extensions have always included hypotheses on the rings, and the theorems involve only binary quadratic forms satisfying further hypotheses. We give a complete statement of the relationship between binary quadratic forms and modules for quadratic algebras over any base ring, or in fact base scheme. The result includes all binary quadratic forms, and commutes with base change. We give global geometric as well as local explicit descriptions of the relationship between forms and modules.

Affiliated with

Also associated with

No associations

Rating

Gauss composition over an arbitrary base 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 Gauss composition over an arbitrary base, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Gauss composition over an arbitrary base will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-452454