In this manuscript we generalize the Z/p metabelian birational p-adic Section Conjecture for curves, as introduced and proved in Pop [P2], to all complete smooth varieties. As a consequence one gets a minimalistic p-adic analog of the famous Artin–Schreier theorem on the Galois characterization of the orderings of fields.

In this work a complete problem for an unambiguous logspace class is presented. This is surprising since unambiguity is a `promise' or`semantic' concept. These usually lead to classes apparently without complete problems.

We d escribe new methods for the e s t imation of the b o u nds of the coeecients of proper divisors of integer polynomials in one v ariable. There exist classes of poly-nomials for which our estimates are better than those obtained using t he polynomial measure or the 2-weighted norm.

The theory of overconvergent modular symbols was created by Glenn Stevens over 20 years ago, and since then the subject has had many generalizations and applications central to modern number theory (e.g. overconvergent cohomology, eigenvarieties of reductive groups, families of p-adic L-functions, just to name a few). In these notes, rather than give a systematic development of the general theo...

We consider the problem of derandomizing random walks in the Euclidean space R. We show that for k = 2, and in some cases in higher dimensions, such walks can be simulated in Logspace using only poly-logarithmically many truly random bits. As a corollary, we show that the random walk can be deterministically simulated in space O(logn √ log log n), where 1/n is the desired precision of the simul...

In 1957 W.M. Hirsch conjectured that every d-polytope with n facets has edge-diameter at most n ? d. Recently Holt and Klee constructed polytopes which meet this bound for a number of (d; n) pairs with d 13 and for all pairs (14; n). These constructions involve a judicious use of truncation, wedging, and blending on polytopes which already meet the Hirsch bound. In this paper we extend these te...

PURPOSE We aimed to determine whether head elevation during combined spinal-epidural anesthesia (CSE) and Caesarean section provided improved hemodynamics and appropriate sensory block height. MATERIALS AND METHODS Forty-four parous women undergoing CSE for elective Caesarean section were randomly assigned to one of two groups: right lateral (group L) or right lateral and head elevated (group...