scholarly journals IWASAWA THEORY FOR THE SYMMETRIC SQUARE OF A CM MODULAR FORM AT INERT PRIMES

2011 ◽  
Vol 54 (2) ◽  
pp. 241-259
Author(s):  
ANTONIO LEI
Keyword(s):  
Modular Form ◽  
Complex Multiplication ◽  
Iwasawa Theory ◽  
The Other ◽  
Selmer Groups ◽  
Supersingular Primes ◽  
Supersingular Prime ◽  
Symmetric Square ◽  
The One ◽  
Invent Math

AbstractLet f be a modular form with complex multiplication (CM) and p an odd prime that is inert in the CM field. We construct two p-adic L-functions for the symmetric square of f, one of which has the same interpolating properties as the one constructed by Delbourgo and Dabrowski (A. Dabrowski and D. Delbourgo, S-adic L-functions attached to the symmetric square of a newform, Proc. Lond. Math. Soc. 74(3) (1997), 559–611), whereas the other one has a similar interpolating properties but corresponds to a different eigenvalue of the Frobenius. The symmetry between these two p-adic L-functions allows us to define the plus and minus p-adic L-functions à la Pollack (R. Pollack, on the p-adic L-function of a modular form at a supersingular prime, Duke Math. J. 118(3) (2003), 523–558). We also define the plus and minus p-Selmer groups analogous to the ones defined by Kobayashi (S. Kobayashi, Iwasawa theory for elliptic curves at supersingular primes, Invent. Math. 152(1) (2003), 1–36). We explain how to relate these two sets of objects via a main conjecture.

scholarly journals Iwasawa theory for the symmetric square of a modular form

2019 ◽  
Vol 2019 (752) ◽  
pp. 179-210 ◽  
Author(s):  
David Loeffler ◽  
Sarah Livia Zerbes
Keyword(s):  
Modular Form ◽  
Galois Representation ◽  
Euler System ◽  
Iwasawa Theory ◽  
Selmer Groups ◽  
Symmetric Square

Abstract We construct a compatible family of global cohomology classes (an Euler system) for the symmetric square of a modular form, and apply this to bounding Selmer groups of the symmetric square Galois representation and its twists.

scholarly journals Iwasawa Theory of Elliptic Modular Forms Over Imaginary Quadratic Fields at Non-ordinary Primes

2019 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Quadratic Field ◽  
Euler System ◽  
Base Change ◽  
Iwasawa Theory ◽  
Imaginary Quadratic Field ◽  
Selmer Groups ◽  
Imaginary Quadratic Fields ◽  
Elliptic Modular Form

AbstractThis article is a continuation of our previous work [7] on the Iwasawa theory of an elliptic modular form over an imaginary quadratic field $K$, where the modular form in question was assumed to be ordinary at a fixed odd prime $p$. We formulate integral Iwasawa main conjectures at non-ordinary primes $p$ for suitable twists of the base change of a newform $f$ to an imaginary quadratic field $K$ where $p$ splits, over the cyclotomic ${\mathbb{Z}}_p$-extension, the anticyclotomic ${\mathbb{Z}}_p$-extensions (in both the definite and the indefinite cases) as well as the ${\mathbb{Z}}_p^2$-extension of $K$. In order to do so, we define Kobayashi–Sprung-style signed Coleman maps, which we use to introduce doubly signed Selmer groups. In the same spirit, we construct signed (integral) Beilinson–Flach elements (out of the collection of unbounded Beilinson–Flach elements of Loeffler–Zerbes), which we use to define doubly signed $p$-adic $L$-functions. The main conjecture then relates these two sets of objects. Furthermore, we show that the integral Beilinson–Flach elements form a locally restricted Euler system, which in turn allow us to deduce (under certain technical assumptions) one inclusion in each one of the four main conjectures we formulate here (which may be turned into equalities in favorable circumstances).

scholarly journals Iwasawa theory for modular forms at supersingular primes

2011 ◽  
Vol 147 (3) ◽  
pp. 803-838 ◽  
Author(s):  
Antonio Lei
Keyword(s):  
Elliptic Curves ◽  
Modular Forms ◽  
Iwasawa Theory ◽  
Selmer Groups ◽  
Main Conjecture ◽  
Supersingular Primes

AbstractWe generalise works of Kobayashi to give a formulation of the Iwasawa main conjecture for modular forms at supersingular primes. In particular, we give analogous definitions of the plus and minus Coleman maps for normalised new forms of arbitrary weights and relate Pollack’s p-adic L-functions to the plus and minus Selmer groups. In addition, by generalising works of Pollack and Rubin on CM elliptic curves, we prove the ‘main conjecture’ for CM modular forms.

On p-adic height pairings and locally free classgroups of Hopf orders

1998 ◽  
Vol 123 (3) ◽  
pp. 447-459
Author(s):  
A. AGBOOLA
Keyword(s):  
Elliptic Curve ◽  
Quadratic Field ◽  
Homogeneous Spaces ◽  
Complex Multiplication ◽  
Imaginary Quadratic Field ◽  
The Other ◽  
Module Structure ◽  
Galois Module ◽  
Ring Of Integers ◽  
The One

Let E be an elliptic curve with complex multiplication by the ring of integers [Ofr ] of an imaginary quadratic field K. The purpose of this paper is to describe certain connections between the arithmetic of E on the one hand and the Galois module structure of certain arithmetic principal homogeneous spaces arising from E on the other. The present paper should be regarded as a complement to [AT]; we assume that the reader is equipped with a copy of the latter paper and that he is not averse to referring to it from time to time.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Stories and the Self

2020 ◽  
Vol 32 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Stefan Krause ◽  
Markus Appel
Keyword(s):  
Meta Analysis ◽  
The Self ◽  
The Other ◽  
Lower Degree ◽  
Contrast Effects ◽  
Self Perception ◽  
Self Perceptions ◽  
Other Hand ◽  
The One ◽  
Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

Radioimmunotherapy for treatment of acute myeloid leukaemia and myelodysplastic syndrome

2005 ◽  
Vol 44 (03) ◽  
pp. 107-117
Author(s):  
R. G. Meyer ◽  
W. Herr ◽  
A. Helisch ◽  
P. Bartenstein ◽  
I. Buchmann
Keyword(s):  
Acute Myeloid Leukaemia ◽  
Myeloid Leukaemia ◽  
Primary Tumour ◽  
The Other ◽  
Haematopoietic Stem Cell ◽  
Other Hand ◽  
Primary Reduction ◽  
The One ◽  
Acute Myeloid

SummaryThe prognosis of patients with acute myeloid leukaemia (AML) has improved considerably by introduction of aggressive consolidation chemotherapy and haematopoietic stem cell transplantation (SCT). Nevertheless, only 20-30% of patients with AML achieve long-term diseasefree survival after SCT. The most common cause of treatment failure is relapse. Additionally, mortality rates are significantly increased by therapy-related causes such as toxicity of chemotherapy and complications of SCT. Including radioimmunotherapies in the treatment of AML and myelodyplastic syndrome (MDS) allows for the achievement of a pronounced antileukaemic effect for the reduction of relapse rates on the one hand. On the other hand, no increase of acute toxicity and later complications should be induced. These effects are important for the primary reduction of tumour cells as well as for the myeloablative conditioning before SCT.This paper provides a systematic and critical review of the currently used radionuclides and immunoconjugates for the treatment of AML and MDS and summarizes the literature on primary tumour cell reductive radioimmunotherapies on the one hand and conditioning radioimmunotherapies before SCT on the other hand.

Das Ende der Postdemokratie, den Pessimismus überwinden.

2017 ◽  
Vol 47 (188) ◽  
pp. 487-494
Author(s):  
Daniel Mullis
Keyword(s):  
Political Thought ◽  
Social Dynamics ◽  
Social Conditions ◽  
The Other ◽  
Economic Decline ◽  
Far Right ◽  
Windows Of Opportunity ◽  
Political Events ◽  
Political Struggles ◽  
The One

In recent years, political and social conditions have changed dramatically. Many analyses help to capture these dynamics. However, they produce political pessimism: on the one hand there is the image of regression and on the other, a direct link is made between socio-economic decline and the rise of the far-right. To counter these aspects, this article argues that current political events are to be understood less as ‘regression’ but rather as a moment of movement and the return of deep political struggles. Referring to Jacques Ranciere’s political thought, the current conditions can be captured as the ‘end of post-democracy’. This approach changes the perspective on current social dynamics in a productive way. It allows for an emphasis on movement and the recognition of the windows of opportunity for emancipatory struggles.

Tolerance is theoretical and practical principles

1996 ◽  
pp. 13-23
Author(s):  
Mykhailo Babiy
Keyword(s):  
Religious Diversity ◽  
The Other ◽  
Nodal Points ◽  
Characteristic Features ◽  
The One ◽  
Ukrainian Society

Political ideological pluralism, religious diversity are characteristic features of modern Ukrainian society. On the one hand, multiculturalism, socio-political, religious differentiation of the latter appear as important characteristics of its democracy, as a practical expression of freedom, on the other - as a factor that led to the deconsocialization of society, gave rise to "nodal points" of tension, confrontational processes, in particular, in political and religious spheres.

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