2015/09/10 by Erick García Ramírez, Ramírez, Erick García
Mathematics · #03C64 #03C98 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #math.AG #math.LO #msc:03C64 #msc:03C98
paper · pdf · doi:10.48550/arxiv.1509.03238
15 pages
arxiv created 2015/09/10 · arxiv updated 2015/09/11
We introduce tangent cones of subsets of cartesian powers of a real closed field, generalising the notion of the classical tangent cones of subsets of Euclidean space. We then study the impact of non-archimedean stratifications (t-stratifications) on these tangent cones. Our main result is that a t-stratification induces stratifications of the same nature on the tangent cones of a definable set. As a consequence, we show that the archimedean counterpart of a t-stratification induces Whitney stratifications on the tangent cones of a semi-algebraic set. The latter statement is achieved by working with the natural valuative structure of non-standard models of the real field.