scholarly journals Graded and filtered fiber functors on Tannakian categories

2013 ◽  
Vol 14 (1) ◽  
pp. 87-130 ◽  
Author(s):  
Paul Ziegler
Keyword(s):  
Base Scheme ◽  
Tannakian Categories

AbstractWe study fiber functors on Tannakian categories which are equipped with a grading or a filtration. Our goal is to give a comprehensive set of foundational results about such functors. A main result is that each filtration on a fiber functor can be split by a grading fpqc-locally on the base scheme.

Finite Subsghemes of Group Schemes

1970 ◽  
Vol 22 (5) ◽  
pp. 1079-1081 ◽  
Author(s):  
Stephen S. Shatz
Keyword(s):  
Simple Proof ◽  
Group Schemes ◽  
Base Scheme ◽  
Finite Presentation ◽  
Empty Subset

If G is an ordinary group and H is a non-empty subset of G, then there are two elementary criteria for H to be a subgroup of G. The first and more general is that the mapping H × H → G × G → G, via 〈x, y〉 ⟼ xy–1 factor through H. The second is that H be finite and closed under multiplication.In the category of group schemes, if one writes down the hypotheses for the first criterion in diagram form, one can supply the proof by a suitable translation of the classical arguments. The only point that causes any difficulty whatsoever is that one must assume that the structure morphism πH: H → S (S is the base scheme) is an epimorphism in order to factor the identity section through H. The second criterion is also true for group schemes under a mild finite presentation hypothesis. It is our aim to provide a simple proof for the following theorem.

scholarly journals Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

2012 ◽  
Vol 12 (5) ◽  
pp. 1603-1622 ◽  
Author(s):  
Helen C. Yee ◽  
Bjorn Sjögreen ◽  
Abdellah Hadjadj
Keyword(s):  
High Order ◽  
Mixing Layers ◽  
Compressible Turbulence ◽  
Filter Method ◽  
Eighth Order ◽  
Base Scheme ◽  
High Order Schemes ◽  
Supersonic Regime ◽  
Seventh Order ◽  
Fifth Order

AbstractThree high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

scholarly journals Base change for semiorthogonal decompositions

2011 ◽  
Vol 147 (3) ◽  
pp. 852-876 ◽  
Author(s):  
Alexander Kuznetsov
Keyword(s):  
Algebraic Variety ◽  
Base Change ◽  
Derived Category ◽  
Intermediate Step ◽  
Coherent Sheaves ◽  
Base Scheme ◽  
Compatible System ◽  
Perfect Complexes

AbstractLet X be an algebraic variety over a base scheme S and ϕ:T→S a base change. Given an admissible subcategory 𝒜 in 𝒟b(X), the bounded derived category of coherent sheaves on X, we construct under some technical conditions an admissible subcategory 𝒜T in 𝒟b(X×ST), called the base change of 𝒜, in such a way that the following base change theorem holds: if a semiorthogonal decomposition of 𝒟b (X) is given, then the base changes of its components form a semiorthogonal decomposition of 𝒟b (X×ST) . As an intermediate step, we construct a compatible system of semiorthogonal decompositions of the unbounded derived category of quasicoherent sheaves on X and of the category of perfect complexes on X. As an application, we prove that the projection functors of a semiorthogonal decomposition are kernel functors.

scholarly journals Tensor Structure on Smooth Motives

2011 ◽  
Vol 9 (1) ◽  
pp. 57-101 ◽  
Author(s):  
Anandam Banerjee
Keyword(s):  
Characteristic Zero ◽  
Full Subcategory ◽  
Resolution Of Singularities ◽  
Homotopy Category ◽  
Tensor Structure ◽  
Perfect Field ◽  
Base Scheme

AbstractRecently, Bondarko constructed a DG category of motives, whose homotopy category is equivalent to Voevodsky's category of effective geometric motives, assuming resolution of singularities. Soon after, Levine extended this idea to construct a DG category whose homotopy category is equivalent to the full subcategory of motives over a base-scheme S generated by the motives of smooth projective S-schemes, assuming that S is itself smooth over a perfect field. In both constructions, the tensor structure requires ℚ-coefficients. In this article, it is shown how to provide a tensor structure on the homotopy category mentioned above, when S is semi-local and essentially smooth over a field of characteristic zero. This is done by defining a pseudo-tensor structure on the DG category of motives constructed by Levine, which induces a tensor structure on its homotopy category.

scholarly journals On the Structure of Affine Flat Group Schemes Over Discrete Valuation Rings, II

2020 ◽  
Author(s):  
Phùng Hô Hai ◽  
João Pedro dos Santos
Keyword(s):  
Discrete Valuation Ring ◽  
Free Module ◽  
Galois Groups ◽  
Affine Group ◽  
Group Schemes ◽  
Infinite Type ◽  
Discrete Valuation Rings ◽  
Valuation Rings ◽  
D Modules ◽  
Tannakian Categories

Abstract In the first part of this work [ 12], we studied affine group schemes over a discrete valuation ring (DVR) by means of Neron blowups. We also showed how to apply these findings to throw light on the group schemes coming from Tannakian categories of $\mathcal{D}$-modules. In the present work, we follow up this theme. We show that a certain class of affine group schemes of “infinite type,” Neron blowups of formal subgroups, are quite typical. We also explain how these group schemes appear naturally in Tannakian categories of $\mathcal{D}$-modules. To conclude, we isolate a Tannakian property of affine group schemes, named prudence, which allows one to verify if the underlying ring of functions is a free module over the base ring. This is then successfully applied to obtain a general result on the structure of differential Galois groups over complete DVRs.

Transient Analysis of a Cylindrical Heat Pipe Considering Different Wick Structures

2016 ◽  
Author(s):  
Mehdi Famouri ◽  
M. Mahdi Abdollahzadeh ◽  
Ahmed Abdulshaheed ◽  
GuangHan Huang ◽  
Gerardo Carbajal ◽  
...  
Keyword(s):  
Heat Pipe ◽  
Experimental Studies ◽  
Simple Algorithm ◽  
Heat Pipes ◽  
Working Fluid ◽  
Time Step ◽  
Base Scheme ◽  
The Stability ◽  
Stability And Accuracy ◽  
Energy Equations

Heat pipes have been shown to be one of the most efficient passive cooling devices for electronic cooling. Only a handful of studies were capable of solving transient performances of heat pipes based on realistic assumptions. A segregated finite volume base scheme using SIMPLE algorithm is used along with system pressurization and overall mass balance to solve mass transfer at the interface, continuity, momentum and energy equations. The fluid flow and heat transfer are solved throughout the wick and vapor core and no assumptions are made at the locations where evaporation and condensations occur. Water is the working fluid and variable densities are used for both liquid and vapor phases to account for continuity at the interface as well as inside of wick and vapor core. The wick is modeled as a non-homogeneous porous media and the effective thermal conductivities and viscous properties are calculated for each type of structure separately using the available relations from the literature. In this study, an axisymmetric two-dimensional solver for cylindrical heat pipe is developed using FLUENT package with the help of User Defined Functions (UDFs) and User Defined Scalar (UDS). The model is tested for grid and time step independency and the results show the stability and accuracy of the proposed method. The numerical results of the present study were in good agreement with the data from previous numerical and experimental studies available in the literature. Additionally, two different wick structures were studied to determine its effect on the thermal performance of heat pipes.

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