In [1], Berger and Colmez introduced a theory of families of étale (φ,Γ)-modules associated to families of p-adic Galois representations. Inspired by their works, we consider families of φ-modules over a reduced affinoid algebra where the base is fixed by Frobenius actions. We prove some results in this framework including the semicontinuity of variation of HN-polygons. These results will be ap...

Let X be a p-divisible group over a regular scheme S such that the Newton polygon in each geometric point of S is the same. Then there is a p-divisible group isogenous to X which has a slope filtration.

For years, the scientific and medical communities have pondered the role of triglycerides in cardiovascular disease (CVD) and mortality risk. Although several studies have shown a relationship between elevated triglyceride levels and CVD, the degree to which triglycerides are independently associated and whether triglycerides directly cause CVD has been hotly debated. This is in contradistincti...

We give a “second generation” exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.

The achievement of adequate and prompt myocardial reperfusion in acute myocardial infarction (AMI) is the most important determinant of recovery of ventricular function at follow-up. This explains the great attention given to the so-called no-reflow phenomenon, which is associated with extensive myocardial damage and a high prevalence of future cardiac events after AMI. The no-reflow phenomenon...