Classification of p-divisible groups

1972 ◽  
pp. 73-93
Author(s):  
Michel Demazure
Keyword(s):  
Divisible Groups

scholarly journals 2-ADIC INTEGRAL CANONICAL MODELS

2016 ◽  
Vol 4 ◽  
Author(s):  
WANSU KIM ◽  
KEERTHI MADAPUSI PERA
Keyword(s):  
Shimura Varieties ◽  
Canonical Models ◽  
Divisible Groups

We use Lau’s classification of 2-divisible groups using Dieudonné displays to construct integral canonical models for Shimura varieties of abelian type at 2-adic places where the level is hyperspecial.

ON -DIVISIBLE GROUPS WITH SATURATED NEWTON POLYGONS

2017 ◽  
Vol 232 ◽  
pp. 96-120
Author(s):  
SHUSHI HARASHITA
Keyword(s):  
Positive Characteristic ◽  
Newton Polygon ◽  
Divisible Group ◽  
Geometric Proof ◽  
Newton Polygons ◽  
Noetherian Scheme ◽  
Weil Divisor ◽  
Divisible Groups

This paper concerns the classification of isogeny classes of$p$-divisible groups with saturated Newton polygons. Let$S$be a normal Noetherian scheme in positive characteristic$p$with a prime Weil divisor$D$. Let${\mathcal{X}}$be a$p$-divisible group over$S$whose geometric fibers over$S\setminus D$(resp. over$D$) have the same Newton polygon. Assume that the Newton polygon of${\mathcal{X}}_{D}$is saturated in that of${\mathcal{X}}_{S\setminus D}$. Our main result (Corollary 1.1) says that${\mathcal{X}}$is isogenous to a$p$-divisible group over$S$whose geometric fibers are all minimal. As an application, we give a geometric proof of the unpolarized analogue of Oort’s conjecture (Oort, J. Amer. Math. Soc.17(2) (2004), 267–296; 6.9).

The v-topology

2020 ◽  
pp. 149-160
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
General Classification ◽  
Powerful Technique ◽  
Sample Application ◽  
Divisible Groups

This chapter describes the v-topology. It develops a powerful technique for proving results about diamonds. There is a topology even finer than the pro-étale topology, the v-topology, which is reminiscent of the fpqc topology on schemes but which is more “topological” in nature. The class of v-covers is extremely general, which will reduce many proofs to very simple base cases. The chapter provides a sample application of this philosophy by establishing a general classification of p-divisible groups over integral perfectoid rings in terms of Breuil-Kisin-Fargues modules. Another use of the v-topology is to prove that certain pro-étale sheaves on Perf are diamonds without finding an explicit pro-étale cover.

scholarly journals Dieudonné theory over semiperfect rings and perfectoid rings

2018 ◽  
Vol 154 (9) ◽  
pp. 1974-2004 ◽  
Author(s):  
Eike Lau
Keyword(s):  
Divisible Group ◽  
Boundedness Condition ◽  
Group Schemes ◽  
Equivalence Of Categories ◽  
Semiperfect Ring ◽  
Formula Group ◽  
Divisible Groups ◽  
Dieudonne Theory

The Dieudonné crystal of a $p$-divisible group over a semiperfect ring $R$ can be endowed with a window structure. If $R$ satisfies a boundedness condition, this construction gives an equivalence of categories. As an application we obtain a classification of $p$-divisible groups and commutative finite locally free $p$-group schemes over perfectoid rings by Breuil–Kisin–Fargues modules if $p\geqslant 3$.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

Interpreting HVEM of muscle-cell impulse networks

1992 ◽  
Vol 50 (1) ◽  
pp. 126-127
Author(s):  
Paul DeCosta ◽  
Kyugon Cho ◽  
Stephen Shemlon ◽  
Heesung Jun ◽  
Stanley M. Dunn
Keyword(s):  
Structural Analysis ◽  
Muscle Cell ◽  
Electron Micrographs ◽  
Relative Size ◽  
Automatic Classification ◽  
Nerve Fibers ◽  
Analysis Algorithm ◽  
Structural Networks

Introduction: The analysis and interpretation of electron micrographs of cells and tissues, often requires the accurate extraction of structural networks, which either provide immediate 2D or 3D information, or from which the desired information can be inferred. The images of these structures contain lines and/or curves whose orientation, lengths, and intersections characterize the overall network.Some examples exist of studies that have been done in the analysis of networks of natural structures. In, Sebok and Roemer determine the complexity of nerve structures in an EM formed slide. Here the number of nodes that exist in the image describes how dense nerve fibers are in a particular region of the skin. Hildith proposes a network structural analysis algorithm for the automatic classification of chromosome spreads (type, relative size and orientation).

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