Tropical analytic geometry, Newton polygons, and tropical intersections

Mathematics – Algebraic Geometry

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

46 pages, 11 figures

Scientific paper

In this paper we use the connections between tropical algebraic geometry and rigid analytic geometry in order to prove two main results. We use tropical methods to prove a theorem about the Newton polygon for convergent power series in several variables: if f_1,...,f_n are n convergent power series in n variables with coefficients in a non-Archimedean field K, we give a formula for the valuations and multiplicities of the common zeros of f_1,...,f_n. We use rigid-analytic methods to show that stable complete intersections of tropical hypersurfaces compute algebraic multiplicities even when the intersection is not tropically proper. These results are naturally formulated and proved using the theory of tropicalizations of rigid-analytic spaces, as introduced by Einsiedler-Kapranov-Lind [EKL06] and Gubler [Gub07b]. We have written this paper to be as readable as possible both to tropical and arithmetic geometers.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Tropical analytic geometry, Newton polygons, and tropical intersections 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 Tropical analytic geometry, Newton polygons, and tropical intersections, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tropical analytic geometry, Newton polygons, and tropical intersections will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-50344

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.