scholarly journals FUJITA DECOMPOSITION AND MASSEY PRODUCT FOR FIBERED VARIETIES

2021 ◽  
pp. 1-29
Author(s):  
LUCA RIZZI ◽  
FRANCESCO ZUCCONI
Keyword(s):  
General Type ◽  
Structure Theorem ◽  
Smooth Curve ◽  
Local System ◽  
Base Change ◽  
Smooth Variety ◽  
Massey Product

Abstract Let $f\colon X\to B$ be a semistable fibration where X is a smooth variety of dimension $n\geq 2$ and B is a smooth curve. We give the structure theorem for the local system of the relative $1$ -forms and of the relative top forms. This gives a neat interpretation of the second Fujita decomposition of $f_*\omega _{X/B}$ . We apply our interpretation to show the existence, up to base change, of higher irrational pencils and on the finiteness of the associated monodromy representations under natural Castelnuovo-type hypothesis on local subsystems. Finally, we give a criterion to have that X is not of Albanese general type if $B=\mathbb {P}^1$ .

scholarly journals Jumps and Motivic Invariants of Semiabelian Jacobians

2018 ◽  
Vol 2019 (20) ◽  
pp. 6437-6479
Author(s):  
Otto Overkamp
Keyword(s):  
Exact Sequence ◽  
A Priori ◽  
Smooth Curve ◽  
Finite Sequence ◽  
Base Change ◽  
Algebraic Tori ◽  
Neron Models ◽  
Picard Functor ◽  
Separable Extensions ◽  
Néron Models

Abstract We investigate Néron models of Jacobians of singular curves over strictly Henselian discretely valued fields and their behavior under tame base change. For a semiabelian variety, this behavior is governed by a finite sequence of (a priori) real numbers between 0 and 1, called jumps. The jumps are conjectured to be rational, which is known in some cases. The purpose of this paper is to prove this conjecture in the case where the semiabelian variety is the Jacobian of a geometrically integral curve with a push-out singularity. Along the way, we prove the conjecture for algebraic tori which are induced along finite separable extensions and generalize Raynaud’s description of the identity component of the Néron model of the Jacobian of a smooth curve (in terms of the Picard functor of a proper, flat, and regular model) to our situation. The main technical result of this paper is that the exact sequence that decomposes the Jacobian of one of our singular curves into its toric and Abelian parts extends to an exact sequence of Néron models. Previously, only split semiabelian varieties were known to have this property.

Surface Water Temperatures of the Canadian Atlantic Coast

1939 ◽  
Vol 4b (5) ◽  
pp. 378-391 ◽  
Author(s):  
H. B. Hachey
Keyword(s):  
Surface Water ◽  
General Type ◽  
Atlantic Coast ◽  
Smooth Curve ◽  
Temperature Curve

Monthly mean surface water temperatures, based on observations from 1926 to 1935 are used to determine normal monthly mean temperatures for eight points on the Canadian Atlantic coast. Sine curves are found to fit the data for all points, with one exception. The general type of temperature curve determined by daily observations divides the regions of observation into those represented by a smooth curve, those by an erratic type, and those showing sharp but regular changes in temperatures from day to day.

scholarly journals Triviality Properties of Principal Bundles on Singular Curves. II

2020 ◽  
Vol 63 (2) ◽  
pp. 423-433
Author(s):  
P. Belkale ◽  
N. Fakhruddin
Keyword(s):  
Simple Group ◽  
Smooth Curve ◽  
Group Scheme ◽  
Singular Locus ◽  
Cartier Divisor ◽  
Base Change ◽  
Sufficient Condition ◽  
Flat Base ◽  
Simply Connected ◽  
Relative Curve

AbstractFor $G$ a split semi-simple group scheme and $P$ a principal $G$-bundle on a relative curve $X\rightarrow S$, we study a natural obstruction for the triviality of $P$ on the complement of a relatively ample Cartier divisor $D\subset X$. We show, by constructing explicit examples, that the obstruction is nontrivial if $G$ is not simply connected, but it can be made to vanish by a faithfully flat base change, if $S$ is the spectrum of a dvr (and some other hypotheses). The vanishing of this obstruction is shown to be a sufficient condition for étale local triviality if $S$ is a smooth curve, and the singular locus of $X-D$ is finite over $S$.

scholarly journals Facteurs epsilon p-adiques

2008 ◽  
Vol 144 (2) ◽  
pp. 439-483 ◽  
Author(s):  
Adriano Marmora
Keyword(s):  
Residue Field ◽  
Smooth Curve ◽  
Local System ◽  
Product Formula ◽  
Mixed Characteristic ◽  
Characteristic Case ◽  
Rank One ◽  
Epsilon Factors ◽  
Valuation Field ◽  
Field Of Norms

AbstractWe develop and study the epsilon factor of a ‘local system’ of p-adic coefficients over the spectrum of a complete discrete valuation field K with finite residue field of characteristic p>0. In the equal characteristic case, we define the epsilon factor of an overconvergent F-isocrystal over Spec(K), using the p-adic monodromy theorem. We conjecture a global formula, the p-adic product formula, analogous to Deligne’s formula for étale ℓ-adic sheaves proved by Laumon, which explains the importance of this local invariant. Namely, for an overconvergent F-isocrystal over an open subset of a projective smooth curve X, the constant of the functional equation of the L-series is expressed as a product of the local epsilon factors at the points of X. We prove the conjecture for rank-one overconvergent F-isocrystals and for finite unit-root overconvergent F-isocrystals. In the mixed characteristic case, we study the behavior of the epsilon factor by deformation to the field of norms.

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.

Existence

2017 ◽  
Author(s):  
Bernhard M¨uhlherr ◽  
Holger P. Petersson ◽  
Richard M. Weiss
Keyword(s):  
Division Algebra ◽  
Quadratic Forms ◽  
Structure Theorem ◽  
Quadratic Extension ◽  
Quadratic Space ◽  
Division Algebras ◽  
Separable Extension ◽  
Valued Fields ◽  
Quaternion Division Algebra

This chapter proves that Bruhat-Tits buildings exist. It begins with a few definitions and simple observations about quadratic forms, including a 1-fold Pfister form, followed by a discussion of the existence part of the Structure Theorem for complete discretely valued fields due to H. Hasse and F. K. Schmidt. It then considers the generic unramified cases; the generic semi-ramified cases, the generic ramified cases, the wild unramified cases, the wild semi-ramified cases, and the wild ramified cases. These cases range from a unique unramified quadratic space to an unramified separable quadratic extension, a tamely ramified division algebra, a ramified separable quadratic extension, and a unique unramified quaternion division algebra. The chapter also describes ramified quaternion division algebras D₁, D₂, and D₃ over K containing a common subfield E such that E/K is a ramified separable extension.

On Lattice-Ordered Rees Matrix Γ-Semigroups

2013 ◽  
Vol 59 (1) ◽  
pp. 209-218 ◽  
Author(s):  
Kostaq Hila ◽  
Edmond Pisha
Keyword(s):  
Structure Theorem ◽  
Lattice Of Congruences

Abstract The purpose of this paper is to introduce and give some properties of l-Rees matrix Γ-semigroups. Generalizing the results given by Guowei and Ping, concerning the congruences and lattice of congruences on regular Rees matrix Γ-semigroups, the structure theorem of l-congruences lattice of l - Γ-semigroup M = μº(G : I; L; Γe) is given, from which it follows that this l-congruences lattice is distributive.

Smooth curve drawing using a Bessel function

2015 ◽  
Author(s):  
Y. Q. Du ◽  
M. J. Pan ◽  
Q. Li ◽  
L. Li
Keyword(s):  
Bessel Function ◽  
Smooth Curve
Sign in / Sign up

Export Citation Format

Share Document