scholarly journals Characteristic cycle and wild ramification for nearby cycles of étale sheaves

Author(s):  
Haoyu Hu ◽  
Jean-Baptiste Teyssier

Abstract In this article, we give a bound for the wild ramification of the monodromy action on the nearby cycles complex of a locally constant étale sheaf on the generic fiber of a smooth scheme over an equal characteristic trait in terms of Abbes and Saito’s logarithmic ramification filtration. This provides a positive answer to the main conjecture in [24] for smooth morphisms in equal characteristic. We also study the ramification along vertical divisors of étale sheaves on relative curves and abelian schemes over a trait.

2009 ◽  
Vol 8 (4) ◽  
pp. 769-829 ◽  
Author(s):  
Takeshi Saito

AbstractWe propose a geometric method to measure the wild ramification of a smooth étale sheaf along the boundary. Using the method, we study the graded quotients of the logarithmic ramification groups of a local field of characteristic p > 0 with arbitrary residue field. We also define the characteristic cycle of an ℓ-adic sheaf, satisfying certain conditions, as a cycle on the logarithmic cotangent bundle and prove that the intersection with the 0-section computes the characteristic class, and hence the Euler number.


1997 ◽  
Vol 161 ◽  
pp. 203-218 ◽  
Author(s):  
Tobias C. Owen

AbstractThe clear evidence of water erosion on the surface of Mars suggests an early climate much more clement than the present one. Using a model for the origin of inner planet atmospheres by icy planetesimal impact, it is possible to reconstruct the original volatile inventory on Mars, starting from the thin atmosphere we observe today. Evidence for cometary impact can be found in the present abundances and isotope ratios of gases in the atmosphere and in SNC meteorites. If we invoke impact erosion to account for the present excess of129Xe, we predict an early inventory equivalent to at least 7.5 bars of CO2. This reservoir of volatiles is adequate to produce a substantial greenhouse effect, provided there is some small addition of SO2(volcanoes) or reduced gases (cometary impact). Thus it seems likely that conditions on early Mars were suitable for the origin of life – biogenic elements and liquid water were present at favorable conditions of pressure and temperature. Whether life began on Mars remains an open question, receiving hints of a positive answer from recent work on one of the Martian meteorites. The implications for habitable zones around other stars include the need to have rocky planets with sufficient mass to preserve atmospheres in the face of intensive early bombardment.


2002 ◽  
Vol 39 (3-4) ◽  
pp. 361-367
Author(s):  
A. Némethi ◽  
I. Sigray

For a   non-constant polynomial map f: Cn?Cn-1 we consider the monodromy representation on the cohomology group of its generic fiber. The main result of the paper determines its dimension and provides a natural basis for it. This generalizes the corresponding results of [2] or [10], where the case n=2 is solved. As  applications,  we verify the Jacobian conjecture for (f,g) when the generic fiber of f is either rational or elliptic. These are generalizations of the corresponding results of [5], [7], [8], [11] and [12], where the case  n=2 is treated.


Author(s):  
Matti Eklund

What is it for a concept to be normative? Some possible answers are explored and rejected, among them that a concept is normative if it ascribes a normative property. The positive answer defended is that a concept is normative if it is in the right way associated with a normative use. Among issues discussed along the way are the nature of analyticity, and there being a notion of analyticity—what I call semantic analyticity—such that a statement can be analytic in this sense while failing to be true. Considerations regarding thick concepts and slurs are brought to bear on the issues that come up.


Author(s):  
Robert Schütze

Can the judicial creation of the EU internal market be justified? A famous—positive—answer has, in the past, been suggested by Miguel Maduro’s We the Court; and the first section explores the credentials of his ‘majoritarian activism’ thesis. The second section surveys alternative forms of legitimacy, such as ‘output legitimacy’ and ‘messianic legitimacy’, but it also offers a new Kantian approach to the legitimacy question.


Author(s):  
Stuart Gray

How can scholars critically engage premodern Indic traditions without falling prey to Hindu conservatism or Brahmanical-Hindu apologism? This question is pressing for Indic political theory and contemporary Indian democracy because of ethnically exclusivist, Hindu nationalist movements that have emerged in the late twentieth and early twenty-first centuries. This chapter argues that a positive answer to the question must begin by taking seriously the tremendous pluralism in India’s political and philosophical history, which requires systematically engaging with premodern source material and uncovering the internal pluralism within a longer and larger Brahmanical-Hindu tradition of political thought. The author explains how it is both possible and politically necessary to internally subvert Brahmanical-Hindu political thought, which can help diffuse essentialist and exclusivist arguments coming from the Hindu right. Locating such plurality and engaging in internal subversion can help challenge historical justifications for Indian nationalism and contribute to decolonization, thus contesting the Hindu right on its own conceptual and genealogical turf. To advance this argument, the author provides a critical reinterpretation of the infamous “Puruṣa Sūkta,” which is often viewed as the locus classicus of the modern caste system, providing a novel interpretation that challenges caste hierarchy and supplies new resources for democratic thought and practice in India.


2018 ◽  
Vol 30 (4) ◽  
pp. 887-913 ◽  
Author(s):  
Kâzım Büyükboduk ◽  
Antonio Lei

Abstract This is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic {\mathbb{Z}_{p}} -tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson–Flach elements.


Author(s):  
Jonathan Ben-Artzi ◽  
Marco Marletta ◽  
Frank Rösler

AbstractThe question of whether there exists an approximation procedure to compute the resonances of any Helmholtz resonator, regardless of its particular shape, is addressed. A positive answer is given, and it is shown that all that one has to assume is that the resonator chamber is bounded and that its boundary is $${{\mathcal {C}}}^2$$ C 2 . The proof is constructive, providing a universal algorithm which only needs to access the values of the characteristic function of the chamber at any requested point.


2021 ◽  
Vol 80 (Suppl 1) ◽  
pp. 340.1-341
Author(s):  
N. Ziade ◽  
J. El-Hajj ◽  
J. Rassi ◽  
S. Hlais ◽  
C. López-Medina ◽  
...  

Background:In patients with spondyloarthritis (SpA), root joint diseases (RJD), i.e. hip or shoulder involvement, may be associated with a distinct disease phenotype compared to those with other affected joints. The ASAS-PerSpA study (PERipheral involvement in SPondyloArthritis) [1], offers a unique opportunity to study the phenotypes of patients with RJD in a global cohort.Objectives:Primary objective was to compare the clinical characteristics of SpA patients with and without RJD. Secondary objectives were to compare the prevalence of RJD across the different SpA subtypes and the different regions of the world, compare the severity of axial disease as well as the disease burden in SpA patients with and without RJD.Methods:This is a post-hoc analysis of the ASAS-PerSpA study, which included 4,465 patients with any subtype of SpA (axial SpA (axSpA), peripheral SpA (pSpA), psoriatic arthritis (PsA), inflammatory bowel disease associated SpA (IBD-SpA), reactive arthritis (ReA) and Juvenile SpA (Juv-SpA)) according to the rheumatologist’s diagnosis. RJD was defined as a positive answer by the investigator to the following question: “Do you consider that the patient has ever suffered from RJD (e.g. hip, shoulder) related to SpA?” In case of a positive answer, a potential specific treatment (e.g. Total Articular Replacement) was investigated. The patient’s characteristics were compared between those with and without RJD involvement, using Chi-2 or Fisher exact test for the categorical variables and t-test for the continuous variables. Two separate multivariable stepwise binary logistic regression analyses were conducted to identify factors associated with the dependent variables “hip involvement” and “shoulder involvement”.Results:RJD occurred in 1,503 patients (33.7%), with more prevalent hip (24.2%) than shoulder (13.2%) involvement. The prevalence of RJD as a group was the highest in Juv-SpA (52.7%), followed by pSpA (44.3%) and axSpA (33.9%). The highest prevalence of RJD was found in Asia and the lowest in Europe and North America. Among patients with hip involvement, 6.0% had a history of hip replacement (highest in the Middle East and North Africa and Latin America); among patients with shoulder involvement, 0.8% had a history of shoulder replacement. Hip had a distinct pattern of associations compared to shoulder involvement (Figure 1). Hip involvement was significantly associated with the SpA main diagnosis (highest in pSpA, lowest in PsA), younger age at first SpA symptom, lower prevalence of family history of psoriasis, positive HLA-B27, occiput-to-wall distance>0, and treatment with cs-DMARDs and b-DMARDs. Shoulder involvement was associated with the SpA main diagnosis (highest in Juv-SpA and pSpA, lowest in axSpA), older age at first SpA symptom, higher prevalence of enthesitis, dactylitis, tender joints count, IBD, occiput-to-wall distance>0, EQ5D score and treatment with cs-DMARDs.Conclusion:Hip involvement was more prevalent than shoulder involvement in patients with SpA, and had a distinct phenotype resembling axial disease whereas shoulder involvement was mostly associated with features of peripheral disease. Hip and shoulder involvement should be analyzed separately in future studies rather than under the RJD entity.References:[1]Lopez-medina, C. et al. Prevalence and Distribution of Peripheral Musculoskeletal Manifestations in Axial Spondyloarthritis, Peripheral Spondyloarthritis and Psoriatic Arthritis: Results of the International, Cross-sectional ASAS-PerSpA Study. RMD Open; 2021;7:e001450.Disclosure of Interests:None declared


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