T. Henkel | Searcharxiv

arXiv2020

A Note on Dieudonné Theory over Perfectoid Rings

For a perfectoid ring $R$ and a natural number $n$ we investigate the essential image of the category of truncated by $n$ Barsotti-Tate groups under the anti-equivalence between commutative, finite, locally free, $R$-group schemes of $p$-power order and torsion Breuil-Kisin-Fargues modules over $R$. We describe the associated semi-liner algebra data and show as a consequence that every $\text{BT}_n$-group over $R$ is the $p^n$-torsion of some $\text{BT}$-group.

math.AG↗

arXiv2014

An Open Mapping Theorem for rings which have a zero sequence of units

This paper provides an Open Mapping Theorem for topological modules over rings that have a zero sequence consisting of units. As an application it is shown that there is a unique complete and metrisable topology on finitely generated modules over certain topological rings (e.g. over complete noetherian Hausdorff Tate rings).

math.FA↗

arXiv2007

3D Simulations of Electromagnetic Fields in Nanostructures using the Time-Harmonic Finite-Element Method

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and optics design of nanostructured components. As has been shown in previous benchmarks some of the presently used methods suffer from low convergence rates and/or low accuracy of the results and exhibit very long computation times which makes application to extended 2D layout patterns impractical. We address 3D simulation tasks by using a finite-element solver which has been shown to be superior to competing methods by several orders of magnitude in accuracy and computational time for typical microlithography simulations. We report on the current status of the solver, incorporating higher order edge elements, adaptive refinement methods, and fast solution algorithms. Further, we investigate the performance of the solver in the 3D simulation project of light diffraction off an alternating phase-shift contact-hole mask.

physics.optics↗