Braid monodromies on proper curves and pro-ℓ Galois representations

2011 ◽  
Vol 11 (1) ◽  
pp. 161-188 ◽  
Author(s):  
Naotake Takao
Keyword(s):  
Galois Representations ◽  
Galois Representation ◽  
Number Fields ◽  
Mapping Class ◽  
Algebraic Number Fields ◽  
Universal Family ◽  
Hyperbolic Curve ◽  
Graded Lie Algebra ◽  
The One ◽  
First Time

AbstractLetCbe a proper smooth geometrically connected hyperbolic curve over a field of characteristic 0 and ℓ a prime number. We prove the injectivity of the homomorphism from the pro-ℓ mapping class group attached to the two dimensional configuration space ofCto the one attached toC, induced by the natural projection. We also prove a certain graded Lie algebra version of this injectivity. Consequently, we show that the kernel of the outer Galois representation on the pro-ℓ pure braid group onCwithnstrings does not depend onn, even ifn= 1. This extends a previous result by Ihara–Kaneko. By applying these results to the universal family over the moduli space of curves, we solve completely Oda's problem on the independency of certain towers of (infinite) algebraic number fields, which has been studied by Ihara, Matsumoto, Nakamura, Ueno and the author. Sequentially we obtain certain information of the image of this Galois representation and get obstructions to the surjectivity of the Johnson–Morita homomorphism at each sufficiently large even degree (as Oda predicts), for the first time for a proper curve.

scholarly journals Nearly ordinary Galois deformations over arbitrary number fields

2008 ◽  
Vol 8 (1) ◽  
pp. 99-177 ◽  
Author(s):  
Frank Calegari ◽  
Barry Mazur
Keyword(s):  
Arbitrary Number ◽  
Quadratic Field ◽  
Galois Representations ◽  
Galois Representation ◽  
Number Fields ◽  
Base Change ◽  
Deformation Spaces ◽  
Totally Real ◽  
Set Of Points ◽  
Dense Set

AbstractLet K be an arbitrary number field, and let ρ : Gal($\math{\bar{K}}$/K) → GL2(E) be a nearly ordinary irreducible geometric Galois representation. In this paper, we study the nearly ordinary deformations of ρ. When K is totally real and ρ is modular, results of Hida imply that the nearly ordinary deformation space associated to ρ contains a Zariski dense set of points corresponding to ‘automorphic’ Galois representations. We conjecture that if K is not totally real, then this is never the case, except in three exceptional cases, corresponding to: (1) ‘base change’, (2) ‘CM’ forms, and (3) ‘even’ representations. The latter case conjecturally can only occur if the image of ρ is finite. Our results come in two flavours. First, we prove a general result for Artin representations, conditional on a strengthening of the Leopoldt Conjecture. Second, when K is an imaginary quadratic field, we prove an unconditional result that implies the existence of ‘many’ positive-dimensional components (of certain deformation spaces) that do not contain infinitely many classical points. Also included are some speculative remarks about ‘p-adic functoriality’, as well as some remarks on how our methods should apply to n-dimensional representations of Gal($\math{\bar{\QQ}}$/ℚ) when n > 2.

scholarly journals Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

2011 ◽  
Vol 203 ◽  
pp. 47-100 ◽  
Author(s):  
Yuichiro Hoshi
Keyword(s):  
Isomorphism Class ◽  
Galois Representations ◽  
Complex Multiplication ◽  
Galois Representation ◽  
Genus Zero ◽  
Isomorphism Classes ◽  
Tate Module ◽  
Hyperbolic Curve ◽  
Theoretic Characterization

AbstractLet l be a prime number. In this paper, we prove that the isomorphism class of an l-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-l outer Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.

scholarly journals Galois-theoretic characterization of isomorphism classes of monodromically full hyperbolic curves of genus zero

2011 ◽  
Vol 203 ◽  
pp. 47-100 ◽  
Author(s):  
Yuichiro Hoshi
Keyword(s):  
Isomorphism Class ◽  
Galois Representations ◽  
Complex Multiplication ◽  
Galois Representation ◽  
Genus Zero ◽  
Isomorphism Classes ◽  
Tate Module ◽  
Hyperbolic Curve ◽  
Theoretic Characterization

AbstractLetlbe a prime number. In this paper, we prove that the isomorphism class of anl-monodromically full hyperbolic curve of genus zero over a finitely generated extension of the field of rational numbers is completely determined by the kernel of the natural pro-louter Galois representation associated to the hyperbolic curve. This result can be regarded as a genus zero analogue of a result due to Mochizuki which asserts that the isomorphism class of an elliptic curve which does not admit complex multiplication over a number field is completely determined by the kernels of the natural Galois representations on the various finite quotients of its Tate module.

scholarly journals On mod local-global compatibility for in the ordinary case

2017 ◽  
Vol 153 (11) ◽  
pp. 2215-2286 ◽  
Author(s):  
Florian Herzig ◽  
Daniel Le ◽  
Stefano Morra
Keyword(s):  
Unitary Group ◽  
Automorphic Forms ◽  
Galois Representations ◽  
Galois Representation ◽  
Number Fields ◽  
Serre's Conjecture ◽  
Ordinary Case ◽  
Serre’S Conjecture ◽  
The Way

Suppose that $F/F^{+}$ is a CM extension of number fields in which the prime $p$ splits completely and every other prime is unramified. Fix a place $w|p$ of $F$. Suppose that $\overline{r}:\operatorname{Gal}(\overline{F}/F)\rightarrow \text{GL}_{3}(\overline{\mathbb{F}}_{p})$ is a continuous irreducible Galois representation such that $\overline{r}|_{\operatorname{Gal}(\overline{F}_{w}/F_{w})}$ is upper-triangular, maximally non-split, and generic. If $\overline{r}$ is automorphic, and some suitable technical conditions hold, we show that $\overline{r}|_{\operatorname{Gal}(\overline{F}_{w}/F_{w})}$ can be recovered from the $\text{GL}_{3}(F_{w})$-action on a space of mod $p$ automorphic forms on a compact unitary group. On the way we prove results about weights in Serre’s conjecture for $\overline{r}$, show the existence of an ordinary lifting of $\overline{r}$, and prove the freeness of certain Taylor–Wiles patched modules in this context. We also show the existence of many Galois representations $\overline{r}$ to which our main theorem applies.

DEFORMATIONS OF GALOIS REPRESENTATIONS AND THE THEOREMS OF SATO–TATE AND LANG–TROTTER

2011 ◽  
Vol 07 (08) ◽  
pp. 2065-2079
Author(s):  
AFTAB PANDE
Keyword(s):  
Galois Representations ◽  
Galois Representation ◽  
Number Fields

We construct infinitely ramified Galois representations ρ such that the al(ρ)'s have distributions in contrast to the statements of Sato–Tate, Lang–Trotter and others. Using similar methods we deform a residual Galois representation for number fields and obtain an infinitely ramified representation with very large image, generalizing a result of Ramakrishna.

scholarly journals Images of Galois representations in mod p Hecke algebras

2020 ◽  
pp. 1-21
Author(s):  
Laia Amorós
Keyword(s):  
Finite Field ◽  
Commutative Algebra ◽  
Galois Representations ◽  
Residue Field ◽  
Representation Formula ◽  
Galois Representation ◽  
Number Fields ◽  
Abelian Extensions ◽  
Hecke Eigenform ◽  
Coefficient Ring

Let [Formula: see text] denote the mod [Formula: see text] local Hecke algebra attached to a normalized Hecke eigenform [Formula: see text], which is a commutative algebra over some finite field [Formula: see text] of characteristic [Formula: see text] and with residue field [Formula: see text]. By a result of Carayol we know that, if the residual Galois representation [Formula: see text] is absolutely irreducible, then one can attach to this algebra a Galois representation [Formula: see text] that is a lift of [Formula: see text]. We will show how one can determine the image of [Formula: see text] under the assumptions that (i) the image of the residual representation contains [Formula: see text], (ii) [Formula: see text] and (iii) the coefficient ring is generated by the traces. As an application we will see that the methods that we use allow to deduce the existence of certain [Formula: see text]-elementary abelian extensions of big non-solvable number fields.

scholarly journals Irreducibility of mod p Galois representations of elliptic curves with multiplicative reduction over number fields

2021 ◽  
pp. 1-10
Author(s):  
Filip Najman ◽  
George C. Ţurcaş
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Number Field ◽  
Galois Representations ◽  
Galois Representation ◽  
Number Fields ◽  
Fermat's Last Theorem ◽  
Modular Method ◽  
Explicit Constant ◽  
Mod P

In this paper we prove that for every integer [Formula: see text], there exists an explicit constant [Formula: see text] such that the following holds. Let [Formula: see text] be a number field of degree [Formula: see text], let [Formula: see text] be any rational prime that is totally inert in [Formula: see text] and [Formula: see text] any elliptic curve defined over [Formula: see text] such that [Formula: see text] has potentially multiplicative reduction at the prime [Formula: see text] above [Formula: see text]. Then for every rational prime [Formula: see text], [Formula: see text] has an irreducible mod [Formula: see text] Galois representation. This result has Diophantine applications within the “modular method”. We present one such application in the form of an Asymptotic version of Fermat’s Last Theorem that has not been covered in the existing literature.

scholarly journals Atlas of ticks (Acari: Argasidae, Ixodidae) in Germany

2021 ◽  
Author(s):  
Franz Rubel ◽  
Katharina Brugger ◽  
Lidia Chitimia-Dobler ◽  
Hans Dautel ◽  
Elisabeth Meyer-Kayser ◽  
...  
Keyword(s):  
Tick Species ◽  
Migratory Birds ◽  
Dermacentor Reticulatus ◽  
Ixodid Ticks ◽  
Federal States ◽  
Ixodes Frontalis ◽  
Argas Reflexus ◽  
The One ◽  
Argasid Tick ◽  
First Time

AbstractAn updated and increased compilation of georeferenced tick locations in Germany is presented here. This data collection extends the dataset published some years ago by another 1448 new tick locations, 900 locations of which were digitized from literature and 548 locations are published here for the first time. This means that a total of 3492 georeferenced tick locations is now available for Germany. The tick fauna of Germany includes two species of Argasidae in the genera Argas and Carios and 19 species of Ixodidae in the genera Dermacentor, Haemaphysalis, and Ixodes, altogether 21 tick species. In addition, three species of Ixodidae in the genera Hyalomma (each spring imported by migratory birds) and Rhipicephalus (occasionally imported by dogs returning from abroad with their owners) are included in the tick atlas. Of these, the georeferenced locations of 23 tick species are depicted in maps. The occurrence of the one remaining tick species, the recently described Ixodes inopinatus, is given at the level of the federal states. The most common and widespread tick species is Ixodes ricinus, with records in all 16 federal states. With the exception of Hamburg, Dermacentor reticulatus was also found in all federal states. The occurrence of the ixodid ticks Ixodes canisuga, Ixodes frontalis, Ixodes hexagonus and I. inopinatus were documented in at least 11 federal states each. The two mentioned argasid tick species were also documented in numerous federal states, the pigeon tick Argas reflexus in 11 and the bat tick Carios vespertilionis in seven federal states. The atlas of ticks in Germany and the underlying digital dataset in the supplement can be used to improve global tick maps or to study the effects of climate change and habitat alteration on the distribution of tick species.

Intuitionistic fuzzy two-factor variance analysis of movie ticket sales

2021 ◽  
pp. 1-11
Author(s):  
Velichka Traneva ◽  
Stoyan Tranev
Keyword(s):  
Comparative Analysis ◽  
Real Data ◽  
Intuitionistic Fuzzy Sets ◽  
Real Numbers ◽  
Data Set ◽  
Important Method ◽  
Ticket Sales ◽  
Intuitionistic Fuzzy ◽  
The One ◽  
First Time

Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.

scholarly journals Experiential ownership and body ownership are different phenomena

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Caleb Liang ◽  
Wen-Hsiang Lin ◽  
Tai-Yuan Chang ◽  
Chi-Hong Chen ◽  
Chen-Wei Wu ◽  
...  
Keyword(s):  
Conscious Experience ◽  
Distinct Type ◽  
Body Part ◽  
The Body ◽  
Body Ownership ◽  
Rubber Hand ◽  
Person Perspective ◽  
The One ◽  
First Time ◽  
Full Body

AbstractBody ownership concerns what it is like to feel a body part or a full body as mine, and has become a prominent area of study. We propose that there is a closely related type of bodily self-consciousness largely neglected by researchers—experiential ownership. It refers to the sense that I am the one who is having a conscious experience. Are body ownership and experiential ownership actually the same phenomenon or are they genuinely different? In our experiments, the participant watched a rubber hand or someone else’s body from the first-person perspective and was touched either synchronously or asynchronously. The main findings: (1) The sense of body ownership was hindered in the asynchronous conditions of both the body-part and the full-body experiments. However, a strong sense of experiential ownership was observed in those conditions. (2) We found the opposite when the participants’ responses were measured after tactile stimulations had ceased for 5 s. In the synchronous conditions of another set of body-part and full-body experiments, only experiential ownership was blocked but not body ownership. These results demonstrate for the first time the double dissociation between body ownership and experiential ownership. Experiential ownership is indeed a distinct type of bodily self-consciousness.

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