Shtukas with one leg

2020 ◽  
pp. 98-107
Author(s):  
Peter Scholze ◽  
Jared Weinstein
Keyword(s):  
Hodge Theory ◽  
Formal Schemes ◽  
Geometric Point ◽  
Divisible Groups ◽  
Special Case ◽  
General Connection

This chapter analyzes shtukas with one leg over a geometric point in detail, and discusses the relation to (integral) p-adic Hodge theory. It focuses on the connection between shtukas with one leg and p-divisible groups, and recovers a result of Fargues which states that p-divisible groups are equivalent to one-legged shtukas of a certain kind. In fact this is a special case of a much more general connection between shtukas with one leg and proper smooth (formal) schemes. Throughout, the goal is to fix an algebraically closed nonarchimedean field. The chapter then provides an overview of shtukas with one leg and p-divisible groups.

scholarly journals RAPOPORT–ZINK SPACES OF HODGE TYPE

2018 ◽  
Vol 6 ◽  
Author(s):  
WANSU KIM
Keyword(s):  
Shimura Varieties ◽  
Formal Schemes ◽  
Divisible Groups ◽  
Extra Structure

When$p>2$, we construct a Hodge-type analogue of Rapoport–Zink spaces under the unramifiedness assumption, as formal schemes parametrizing ‘deformations’ (up to quasi-isogeny) of$p$-divisible groups with certain crystalline Tate tensors. We also define natural rigid analytic towers with expected extra structure, providing more examples of ‘local Shimura varieties’ conjectured by Rapoport and Viehmann.

-DISPLAYS AND RAPOPORT–ZINK SPACES

2018 ◽  
Vol 19 (4) ◽  
pp. 1211-1257 ◽  
Author(s):  
O. Bültel ◽  
G. Pappas
Keyword(s):  
Reductive Group ◽  
Witt Vector ◽  
Formal Schemes ◽  
Divisible Groups

Let $(G,\unicode[STIX]{x1D707})$ be a pair of a reductive group $G$ over the $p$-adic integers and a minuscule cocharacter $\unicode[STIX]{x1D707}$ of $G$ defined over an unramified extension. We introduce and study ‘$(G,\unicode[STIX]{x1D707})$-displays’ which generalize Zink’s Witt vector displays. We use these to define certain Rapoport–Zink formal schemes purely group theoretically, i.e. without $p$-divisible groups.

scholarly journals Rolling of a body on a plane or a sphere: a geometric point of view

2004 ◽  
Vol 70 (2) ◽  
pp. 245-256 ◽  
Author(s):  
S. Reza Moghadasi
Keyword(s):  
Control Theory ◽  
Nonholonomic Systems ◽  
Point Of View ◽  
Global Approach ◽  
Geometric Point ◽  
Special Case

A pair of bodies rolling on each other is an interesting example of nonholonomic systems in control theory. Here the controllability of rolling bodies is investigated with a global approach. By using simple geometric facts, this problem has been completely solved in the special case where one of them is a plane or a sphere.

scholarly journals Rapoport–Zink spaces for spinor groups

2017 ◽  
Vol 153 (5) ◽  
pp. 1050-1118 ◽  
Author(s):  
Benjamin Howard ◽  
Georgios Pappas
Keyword(s):  
General Theory ◽  
Shimura Varieties ◽  
Good Theory ◽  
Good Reduction ◽  
Formal Schemes ◽  
Special Case ◽  
Canonical Integral

After the work of Kisin, there is a good theory of canonical integral models of Shimura varieties of Hodge type at primes of good reduction. The first part of this paper develops a theory of Hodge type Rapoport–Zink formal schemes, which uniformize certain formal completions of such integral models. In the second part, the general theory is applied to the special case of Shimura varieties associated with groups of spinor similitudes, and the reduced scheme underlying the Rapoport–Zink space is determined explicitly.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

Determination of the phase structure of polymerblends by electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 492-493
Author(s):  
Dr. G. Kaemof
Keyword(s):  
Screw Extruder ◽  
Electron Microscopic ◽  
Thin Sections ◽  
Single Screw Extruder ◽  
Transmission Electron ◽  
The Matrix ◽  
Twin Screw ◽  
Special Case ◽  
Microscopic Investigations

A mixture of polycarbonate (PC) and styrene-acrylonitrile-copolymer (SAN) represents a very good example for the efficiency of electron microscopic investigations concerning the determination of optimum production procedures for high grade product properties.The following parameters have been varied:components of charge (PC : SAN 50 : 50, 60 : 40, 70 : 30), kind of compounding machine (single screw extruder, twin screw extruder, discontinuous kneader), mass-temperature (lowest and highest possible temperature).The transmission electron microscopic investigations (TEM) were carried out on ultra thin sections, the PC-phase of which was selectively etched by triethylamine.The phase transition (matrix to disperse phase) does not occur - as might be expected - at a PC to SAN ratio of 50 : 50, but at a ratio of 65 : 35. Our results show that the matrix is preferably formed by the components with the lower melting viscosity (in this special case SAN), even at concentrations of less than 50 %.

Test Validation Without Measurement

2016 ◽  
Vol 32 (3) ◽  
pp. 204-214 ◽  
Author(s):  
Emilie Lacot ◽  
Mohammad H. Afzali ◽  
Stéphane Vautier
Keyword(s):  
Test Data ◽  
Test Scores ◽  
Scientific Explanation ◽  
Test Validation ◽  
Clinical Tests ◽  
Ethical Perspective ◽  
Power Of Test ◽  
Memory Accuracy ◽  
Social Uses ◽  
Special Case

Abstract. Test validation based on usual statistical analyses is paradoxical, as, from a falsificationist perspective, they do not test that test data are ordinal measurements, and, from the ethical perspective, they do not justify the use of test scores. This paper (i) proposes some basic definitions, where measurement is a special case of scientific explanation; starting from the examples of memory accuracy and suicidality as scored by two widely used clinical tests/questionnaires. Moreover, it shows (ii) how to elicit the logic of the observable test events underlying the test scores, and (iii) how the measurability of the target theoretical quantities – memory accuracy and suicidality – can and should be tested at the respondent scale as opposed to the scale of aggregates of respondents. (iv) Criterion-related validity is revisited to stress that invoking the explanative power of test data should draw attention on counterexamples instead of statistical summarization. (v) Finally, it is argued that the justification of the use of test scores in specific settings should be part of the test validation task, because, as tests specialists, psychologists are responsible for proposing their tests for social uses.

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