We prove a geometric logarithmic derivative lemma for rigid analytic mappings to algebraic varieties in characteristic zero. We use the lemma to give a new and simpler proof (at least in characteristic zero) of Berkovich’s little Picard theorem, which says there are no nonconstant rigid analytic maps from the affine line to nonsingular projective curves of positive genus, and of Cherry’s result...

semi-rigid aluminum containers are being used widely in food industries. they have wrinkle shaped walls for strengthening their physical structure. the objective of this study was to assess the effect of wrinkled parts on the heat transfer and temperature distribution of the containers by computational fluid dynamics (cfd) analysis. therefore, a precise designed geometry of the wrinkled walls c...

To compensate for soft-tissue deformation during image-guided surgical procedures, non-rigid methods are often used as compensation. However, most of these algorithms first implement a rigid registration to provide an initial alignment. In liver tumor resections, the organ is deformed on a large scale, causing visual shape change on the organ. Unlike neurosurgery, there is no rigid reference av...

The notion of an analytic Zariski structure was introduced in [1] by the author and N.Peatfield in a form slightly different from the one presented here. Analytic Zariski generalises the previously known notion of a Zariski structure (see [2] for one-dimensional case and [3], [4] for the general definition) mainly by dropping the requirement of Noetherianity and weakening the assumptions on the...

The p-adic upper half plane X is a rigid analytic variety over a p-adic field K, on which the group GL2(K) acts, that Mumford introduced (as a formal scheme) as part of his efforts to generalize Tate’s p-adic uniformization of elliptic curves to curves of higher genus. The Cp–valued points of X are just P(Cp)−P(K), with GL2(K) acting by linear fractional transformations. Mumford showed that the...

We present a formal scheme based cycle model for the motivic cohomology of fat points defined by truncated polynomial rings $$k[t]/(t^m)$$ with $$m \ge 2$$ , in one variable over field k. compute their Milnor range class groups when has sufficiently many elements. With some aids from rigid analytic geometry and Gersten conjecture K-theory resolved M. Kerz, we prove that resulting are isomorphic...