scholarly journals Logarithmic Ramifications of Étale Sheaves by Restricting to Curves

2017 ◽  
Vol 2019 (19) ◽  
pp. 5914-5952 ◽  
Author(s):  
Haoyu Hu
Keyword(s):  
Continuity Property ◽  
Smooth Variety ◽  
Swan Conductor ◽  
Lower Semi ◽  
Ramification Theory

Abstract In this article, we prove that the Swan conductor of an étale sheaf on a smooth variety defined by Abbes and Saito’s logarithmic ramification theory can be computed by its classical Swan conductors after restricting it to curves. It extends the main result of Barrientos [7] for rank $1$ sheaves. As an application, we give a logarithmic ramification version of generalizations of Deligne and Laumon’s lower semi-continuity property for Swan conductors of étale sheaves on relative curves to higher relative dimensions in a geometric situation.

scholarly journals Semi-continuity for total dimension divisors of étale sheaves

2017 ◽  
Vol 28 (01) ◽  
pp. 1750001
Author(s):  
Haoyu Hu ◽  
Enlin Yang
Keyword(s):  
Continuity Property ◽  
Lower Semi ◽  
Total Dimension

In this paper, we extend an inequality that compares the pull-back of the total dimension divisor of an étale sheaf and the total dimension divisor of the pull-back of the sheaf due to Saito. Using this formula, we generalize Deligne and Laumon’s lower semi-continuity property for Swan conductors of étale sheaves on relative curves to higher relative dimensions in a geometric situation.

Continuity of homotopies

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Open Subset ◽  
Small Neighborhood ◽  
Unit Vector ◽  
Zariski Topology ◽  
Simple Point ◽  
Smooth Variety ◽  
Additional Material ◽  
Generic Type ◽  
Zariski Open Subset

This chapter includes some additional material on homotopies. In particular, for a smooth variety V, there exists an “inflation” homotopy, taking a simple point to the generic type of a small neighborhood of that point. This homotopy has an image that is properly a subset of unit vector V, and cannot be understood directly in terms of definable subsets of V. The image of this homotopy retraction has the merit of being contained in unit vector U for any dense Zariski open subset U of V. The chapter also proves the continuity of functions and homotopies using continuity criteria and constructs inflation homotopies before proving GAGA type results for connectedness. Additional results regarding the Zariski topology are given.

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

Convex extensions and envelopes of lower semi-continuous functions

2002 ◽  
Vol 93 (2) ◽  
pp. 247-263 ◽  
Author(s):  
Mohit Tawarmalani ◽  
Nikolaos V Sahinidis
Keyword(s):  
Continuous Functions ◽  
Lower Semi

On Ramification Theory in Noetherian Rings

1959 ◽  
Vol 81 (3) ◽  
pp. 749 ◽  
Author(s):  
M. Auslander ◽  
D. A. Buchsbaum
Keyword(s):  
Noetherian Rings ◽  
Ramification Theory

scholarly journals A Fenchel-Rockafellar type duality theorem for maximization

1979 ◽  
Vol 20 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Ivan Singer
Keyword(s):  
Convex Space ◽  
Duality Theorem ◽  
Locally Convex Space ◽  
Bounded Subset ◽  
Convex Functional ◽  
Lower Semi ◽  
Locally Convex

We prove that sup(f-h)(E) = sup(h*-f*)(E*), where f is a proper lower semi-continuous convex functional on a real locally convex space E, h: E → = [-∞, +∞] is an arbitrary-functional and, f*, h* are their convex conjugates respectively. When h = δG, the indicator of a bounded subset G of E, this yields a formula for sup f(G).

scholarly journals On a new structure of the pantograph inclusion problem in the Caputo conformable setting

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sabri T. M. Thabet ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Differential Equation ◽  
Inclusion Problem ◽  
Integral Conditions ◽  
Lower Semi ◽  
First Time ◽  
Existence Criteria

Abstract In this work, we reformulate and investigate the well-known pantograph differential equation by applying newly-defined conformable operators in both Caputo and Riemann–Liouville settings simultaneously for the first time. In fact, we derive the required existence criteria of solutions corresponding to the inclusion version of the three-point Caputo conformable pantograph BVP subject to Riemann–Liouville conformable integral conditions. To achieve this aim, we establish our main results in some cases including the lower semi-continuous, the upper semi-continuous and the Lipschitz set-valued maps. Eventually, the last part of the present research is devoted to proposing two numerical simulative examples to confirm the consistency of our findings.

scholarly journals On the Notion of Conductor in the Local Geometric Langlands Correspondence

2017 ◽  
Vol 69 (1) ◽  
pp. 107-129
Author(s):  
Masoud Kamgarpour
Keyword(s):  
Irreducible Representation ◽  
Galois Representation ◽  
Loop Group ◽  
Langlands Correspondence ◽  
Categorical Representation ◽  
Swan Conductor ◽  
Geometric Langlands ◽  
Meromorphic Connection ◽  
Local Langlands Correspondence ◽  
Geometric Analogue

AbstractUnder the local Langlands correspondence, the conductor of an irreducible representation of Gln(F) is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.

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