scholarly journals On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic

2021 ◽  
pp. 1
Author(s):  
Roman Fedorov
Keyword(s):  
Principal Bundles ◽  
Mixed Characteristic

scholarly journals A pathological case of the C1 conjecture in mixed characteristic

2018 ◽  
Vol 167 (01) ◽  
pp. 61-64 ◽  
Author(s):  
INDER KAUR
Keyword(s):  
Line Bundle ◽  
Moduli Space ◽  
Projective Curve ◽  
Free Sheaf ◽  
Smooth Projective Curve ◽  
Mixed Characteristic ◽  
Locally Free Sheaf ◽  
Fixed Rank ◽  
Pathological Case

AbstractLet K be a field of characteristic 0. Fix integers r, d coprime with r ⩾ 2. Let XK be a smooth, projective, geometrically connected curve of genus g ⩾ 2 defined over K. Assume there exists a line bundle ${\cal L}_K$ on XK of degree d. In this paper we prove the existence of a stable locally free sheaf on XK with rank r and determinant ${\cal L}_K$. This trivially proves the C1 conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.

Study on Cavity Growth in Uniaxial Tension of ZK60 Magnesium Alloy

2007 ◽  
Vol 353-358 ◽  
pp. 687-690
Author(s):  
Yan Dong Yu ◽  
De Liang Yin ◽  
Bao You Zhang
Keyword(s):  
Volume Fraction ◽  
Cavity Growth ◽  
Experimental Studies ◽  
Superplastic Forming ◽  
Cavity Radius ◽  
Analysis Software ◽  
Mixed Characteristic ◽  
Substantial Growth ◽  
Zk60 Magnesium Alloy ◽  
Electronic Microscope

Cavity growth is a typical microstructure feature in superplastic forming (SPF) of materials. Substantial growth and interlink of cavities in superplastic deformation usually lead to reduction in elongation, even to failure. Consequently, it is necessary to investigate the mechanism and model of cavity growth. In this paper, experimental studies on cavity growth were carried out by means of superplastic tension of ZK60 magnesium alloys. Scanning electronic microscope (SEM) was employed for observation of fractography. Experimental cavity radius and volume fraction were determined by optical microscopy and corresponding picture-based analysis software. It is found that, the fractured surfaces after a superplastic elongation have a mixed characteristic of intergranular cavities and dimples. Further, the cavity growth is identified to follow a exponentially increasing mode.

scholarly journals Two-Categorical Bundles and their Classifying Spaces

2012 ◽  
Vol 10 (2) ◽  
pp. 299-369 ◽  
Author(s):  
Nils A. Baas ◽  
Marcel Bökstedt ◽  
Tore August Kro
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Vector Spaces ◽  
Bundle Theory ◽  
Classifying Spaces ◽  
Classifying Space ◽  
Principal Bundles

AbstractFor a 2-category 2C we associate a notion of a principal 2C-bundle. For the 2-category of 2-vector spaces, in the sense of M.M. Kapranov and V.A. Voevodsky, this gives the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes. Our main result says that the geometric nerve of a good 2-category is a classifying space for the associated principal 2-bundles. In the process of proving this we develop powerful machinery which may be useful in further studies of 2-categorical topology. As a corollary we get a new proof of the classification of principal bundles. Another 2-category of 2-vector spaces has been proposed by J.C. Baez and A.S. Crans. A calculation using our main theorem shows that in this case the theory of principal 2-bundles splits, up to concordance, as two copies of ordinary vector bundle theory. When 2C is a cobordism type 2-category we get a new notion of cobordism-bundles which turns out to be classified by the Madsen–Weiss spaces.

scholarly journals Double principal bundles

2021 ◽  
pp. 104354
Author(s):  
Honglei Lang ◽  
Yanpeng Li ◽  
Zhangju Liu
Keyword(s):  
Principal Bundles

scholarly journals Normal hyperplane sections of normal schemes in mixed characteristic

2018 ◽  
Vol 47 (6) ◽  
pp. 2412-2425
Author(s):  
Jun Horiuchi ◽  
Kazuma Shimomoto
Keyword(s):  
Mixed Characteristic ◽  
Hyperplane Sections

scholarly journals A motivic version of the theorem of Fontaine and Wintenberger

2018 ◽  
Vol 155 (1) ◽  
pp. 38-88 ◽  
Author(s):  
Alberto Vezzani
Keyword(s):  
Galois Groups ◽  
Rational Homotopy ◽  
Mixed Characteristic ◽  
Homotopy Invariant ◽  
Analytic Varieties

We establish a tilting equivalence for rational, homotopy-invariant cohomology theories defined over non-archimedean analytic varieties. More precisely, we prove an equivalence between the categories of motives of rigid analytic varieties over a perfectoid field $K$ of mixed characteristic and over the associated (tilted) perfectoid field $K^{\flat }$ of equal characteristic. This can be considered as a motivic generalization of a theorem of Fontaine and Wintenberger, claiming that the Galois groups of $K$ and $K^{\flat }$ are isomorphic.

scholarly journals Mukai-Sakai bound for equivariant principal bundles

2005 ◽  
Vol 43 (1) ◽  
pp. 133-141
Author(s):  
Usha N. Bhosle ◽  
Indranil Biswas
Keyword(s):  
Principal Bundles

scholarly journals Criterion for connections on principal bundles over a pointed Riemann surface

2017 ◽  
Vol 4 (1) ◽  
pp. 155-171 ◽  
Author(s):  
Indranil Biswas
Keyword(s):  
Riemann Surface ◽  
Principal Bundles ◽  
Connections On Principal Bundles

Abstract We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.

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