scholarly journals Asymptotic homological conjectures in mixed characteristic

2007 ◽  
Vol 230 (2) ◽  
pp. 427-467 ◽  
Author(s):  
Hans Schoutens
Keyword(s):  
Mixed Characteristic ◽  
Homological Conjectures

Defective big Cohen-Macaulay modules

1983 ◽  
Vol 93 (2) ◽  
pp. 253-257
Author(s):  
M. L. Brown
Keyword(s):  
Local Ring ◽  
Commutative Algebra ◽  
Regular Sequence ◽  
Local Rings ◽  
Mixed Characteristic ◽  
Noetherian Local Ring ◽  
System Of Parameters ◽  
Homological Conjectures

Let R be a noetherian local ring and x = x1, …, xn a system of parameters for R. If R is an equicharacteristic local ring then Hochster(3) proved there is a big Cohen-Macaulay module with respect to x, i.e. an R-module M, not necessarily noetherian, with x1, …, xn a regular sequence on M and M/(x) M ≠ 0. Such modules are important for the study of the homological conjectures in commutative algebra(3). Nevertheless, for mixed characteristic local rings virtually nothing is known about their existence.

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 AUSLANDER GENERATORS AND HOMOLOGICAL CONJECTURES

2013 ◽  
Vol 56 (3) ◽  
pp. 503-506 ◽  
Author(s):  
JIAQUN WEI
Keyword(s):  
Artin Algebra ◽  
Representation Dimension ◽  
Homological Conjectures

AbstractLet A be an artin algebra with representation dimension not more than 3. Assuming that AV is an Auslander generator and M ∈ addAV, we show that both findim(EndAM) and findim(EndAM)op are finite, and consequently the Gorenstein symmetry conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for EndAM.

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 Arithmetic 𝒟-modules on the unit disk. With an appendix by Shigeki Matsuda

2011 ◽  
Vol 148 (1) ◽  
pp. 227-268 ◽  
Author(s):  
Richard Crew
Keyword(s):  
Unit Disk ◽  
Valuation Ring ◽  
Discrete Valuation Ring ◽  
Mixed Characteristic ◽  
Complete Discrete Valuation Ring ◽  
Canonical Extensions

AbstractLet 𝒱 be a complete discrete valuation ring of mixed characteristic. We classify arithmetic 𝒟-modules on Spf(𝒱[[t]]) up to certain kind of ‘analytic isomorphism’. This result is used to construct canonical extensions (in the sense of Katz and Gabber) for objects of this category.

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