Related papers: On log crystalline higher direct image
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
Crystalline graded rings are generalizations of certain classes of rings like generalized twisted group rings, generalized Weyl algebras, and generalized skew crossed products. When the base ring is a commutative Dedekind domain, two…
This note discusses some examples showing that the crystalline cohomology of even very mildly singular projective varieties tends to be quite large. In particular, any singular projective variety with at worst ordinary double points has…
For an arbitrary non-archimedean local field we classify reductive group schemes over the corresponding Fargues-Fontaine curve by group schemes over the category of isocrystals. We then classify torsors under such reductive group schemes by…
In this paper (part of the author's PhD thesis), we introduce the notions of semistability and potential semistability of overconvergent F-crystals over an equal characteristic local field. We establish their equivalence with the notions of…
We introduce and study a log discrepancy function on the space of semivaluations centered on an integral noetherian scheme of positive characteristic. Our definition shares many properties with the analogue in characteristic zero; we prove…
We demonstrate that a hexagonal two dimensional photonic crystal can act as an isotropic medium with an effective refractive index n_eff = -1, therefore capable of unrestricted superlensing. We study the superlensing by calculating the…
We investigate the large intersection properties of the set of points that are approximated at a certain rate by a family of affine subspaces. We then apply our results to various sets arising in the metric theory of Diophantine…
The growth of crystals confined in porous or cellular materials is ubiquitous in Nature and industry. Confinement affects the formation of biominerals in living organisms, of minerals in the Earth's crust and of salt crystals damaging…
A phenomenological theory of luminescence properties of one-dimensional resonant photonic crystals is developed within the framework of classical Maxwell equations with fluctuating polarization terms representing non-coherent sources of…
Let $(A,(p))$ be a crystalline prism with $A_n = A/p^{n+1}A$ for all $n\geq 0$. Let $\frakX_0$ be a smooth scheme over $A_0$. Suppose that $\frakX_0$ admits a lifting $\frakX_n$ over $A_n$ and the absolute Frobenius…
We present an all-dielectric photonic crystal structure that supports two-dimensionally confined helical topological edge states. The topological properties of the system are controlled by the crystal parameters. An interface between two…
We perform extensive monomer-resolved computer simulations of suitably-designed amphiphilic dendritic macromolecules over a broad range of densities, proving the existence and stability of cluster crystals formed in these systems, as…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
Targeting specific technological applications requires the control of nanoparticle properties, especially the crystalline polymorph. Freezing a nanodroplet deposited on a solid substrate leads to the formation of crystalline structures. We…
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree.
Explicit examples of {\bf positive} crystalline measures and Fourier quasicrystals are constructed using pairs of stable of polynomials, answering several open questions in the area.
We prove some new log-free density theorems for zeros of Dirichlet L-functions (which accordingly are more sharp than earlier ones near to the boundary line of the critical strip). The results can be applied in several problems of prime…
TEM images of strained crystals often exhibit symmetries, the source of which is not always clear. To understand these symmetries we distinguish between symmetries that occur from the imaging process itself and symmetries of the inclusion…
We introduce a "limiting Frobenius structure" attached to any degeneration of projective varieties over a finite field of characteristic p which satisfies a p-adic lifting assumption. Our limiting Frobenius structure is shown to be…