Search results for "13a"

showing 10 items of 22 documents

$V$-filtrations in positive characteristic and test modules

2013

Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this coincides with the test module filtration. We also show that the associated graded induces a functor $Gr^{[0,1]}$ from Cartier crystals to Cartier crystals supported on $V(\mathfrak{a})$. This functor commutes with finite pushforwards for principal ideals and with pullbacks along essentially \'etale morphisms. We also derive corresponding transformation rules for test modules generalizing previous results by Schwede and Tucker in the \'etale case (cf. ar…

Primary 13A35 Secondary 14B05General MathematicsType (model theory)Commutative Algebra (math.AC)01 natural sciencesCombinatoricsMathematics - Algebraic GeometryMathematics::Algebraic GeometryMathematics::K-Theory and HomologyMathematics::Category Theory0103 physical sciencesFiltration (mathematics)FOS: MathematicsClosed immersionIdeal (ring theory)0101 mathematicsAlgebraic Geometry (math.AG)MathematicsRing (mathematics)FunctorMathematics::Commutative AlgebraApplied Mathematics010102 general mathematicsMathematics - Commutative AlgebraHypersurface010307 mathematical physicsConstant sheaf
researchProduct

Multiprojective spaces and the arithmetically Cohen-Macaulay property

2019

AbstractIn this paper we study the arithmetically Cohen-Macaulay (ACM) property for sets of points in multiprojective spaces. Most of what is known is for ℙ1× ℙ1and, more recently, in (ℙ1)r. In ℙ1× ℙ1the so called inclusion property characterises the ACM property. We extend the definition in any multiprojective space and we prove that the inclusion property implies the ACM property in ℙm× ℙn. In such an ambient space it is equivalent to the so-called (⋆)-property. Moreover, we start an investigation of the ACM property in ℙ1× ℙn. We give a new construction that highlights how different the behavior of the ACM property is in this setting.

Pure mathematicsArithmetically Cohen-Macaulay multiprojective spacesProperty (philosophy)points in multiprojective spaces arithmetically Cohen-Macaulay linkageGeneral MathematicsStar (graph theory)Space (mathematics)Commutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic Geometryarithmetically Cohen-MacaulayTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY0103 physical sciencesFOS: Mathematics0101 mathematicsAlgebraic Geometry (math.AG)Mathematics010102 general mathematics14M05 13C14 13C40 13H10 13A15Mathematics - Commutative Algebrapoints in multiprojective spacesAmbient spaceSettore MAT/02 - Algebra010307 mathematical physicsSettore MAT/03 - Geometrialinkage
researchProduct

F-signature of pairs and the asymptotic behavior of Frobenius splittings

2012

We generalize $F$-signature to pairs $(R,D)$ where $D$ is a Cartier subalgebra on $R$ as defined by the first two authors. In particular, we show the existence and positivity of the $F$-signature for any strongly $F$-regular pair. In one application, we answer an open question of I. Aberbach and F. Enescu by showing that the $F$-splitting ratio of an arbitrary $F$-pure local ring is strictly positive. Furthermore, we derive effective methods for computing the $F$-signature and the $F$-splitting ratio in the spirit of the work of R. Fedder.

Pure mathematicsGeneral Mathematics13A35 13D40 14B05 13H10010102 general mathematicsSubalgebraLocal ringSplitting primeF-regularCommutative Algebra (math.AC)Mathematics - Commutative AlgebraF-signatureF-splitting ratio01 natural sciencesF-pureMathematics - Algebraic GeometryCartier algebra0103 physical sciencesFOS: Mathematics010307 mathematical physics0101 mathematicsSignature (topology)Algebraic Geometry (math.AG)Mathematics
researchProduct

Functorial Test Modules

2016

In this article we introduce a slight modification of the definition of test modules which is an additive functor $\tau$ on the category of coherent Cartier modules. We show that in many situations this modification agrees with the usual definition of test modules. Furthermore, we show that for a smooth morphism $f \colon X \to Y$ of $F$-finite schemes one has a natural isomorphism $f^! \circ \tau \cong \tau \circ f^!$. If $f$ is quasi-finite and of finite type we construct a natural transformation $\tau \circ f_* \to f_* \circ \tau$.

Pure mathematicsSmooth morphismAlgebra and Number TheoryFunctor13A35 (Primary) 14F10 14B05 (Secondary)010102 general mathematicsType (model theory)Mathematics - Commutative AlgebraCommutative Algebra (math.AC)01 natural sciencesMathematics - Algebraic GeometryTransformation (function)0103 physical sciencesNatural transformationFOS: Mathematics010307 mathematical physics0101 mathematicsAlgebraic Geometry (math.AG)Mathematics
researchProduct

Use of HFC fluids as suitable replacements in low-temperature refrigeration plants

2014

An experimental investigation of the performance of a low-temperature refrigerating unit working with R22 and a comparison of its performance when operating with replacement HFC fluids in accordance with the European Regulation CE-1005/2009 are presented in this paper. Plant working efficiency was tested with R22, as baseline, and then compared with four different HFC fluids: R413A, R417A, R422A and R422D. The refrigerating unit was a vapour-compression plant equipped with a reciprocating double-cylinder compressor able to keep the cold room at -20ºC. Lower values of the temperature at the end of compression and polytrophic exponent can be achieved with the HFC tested. Substituting the R22 …

R422dSettore ING-IND/10 - Fisica Tecnica IndustrialeRefrigerating systemR417aR422aR22R413a
researchProduct

Locally nilpotent derivations of rings graded by an abelian group

2019

International audience

Russel cubic threefoldPure mathematicsAffine algebraic geometryPham-Brieskorn variety010102 general mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Locally nilpotent13A50Locally nilpotent derivation01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Russell cubic threefold0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsAbelian group14R20MSC: Primary 14R20 ; Secondary 13A50ComputingMilieux_MISCELLANEOUSMathematics
researchProduct

Test module filtrations for unit $F$-modules

2015

We extend the notion of test module filtration introduced by Blickle for Cartier modules. We then show that this naturally defines a filtration on unit $F$-modules and prove that this filtration coincides with the notion of $V$-filtration introduced by Stadnik in the cases where he proved existence of his filtration. We also show that these filtrations do not coincide in general. Moreover, we show that for a smooth morphism $f: X \to Y$ test modules are preserved under $f^!$. We also give examples to show that this is not the case if $f$ is finite flat and tamely ramified along a smooth divisor.

Smooth morphismPure mathematicsAlgebra and Number Theory010102 general mathematicsDivisor (algebraic geometry)Commutative Algebra (math.AC)Mathematics - Commutative Algebra01 natural sciencesMathematics - Algebraic GeometryMathematics::Algebraic GeometryMathematics::K-Theory and Homology0103 physical sciencesPrimary 13A35 Secondary 14B05 14F10Filtration (mathematics)FOS: Mathematics010307 mathematical physics0101 mathematicsUnit (ring theory)Algebraic Geometry (math.AG)Mathematics
researchProduct

CCDC 783551: Experimental Crystal Structure Determination

2011

Related Article: Nonappa, K.Ahonen, M.Lahtinen, E.Kolehmainen|2011|Green Chemistry|13|1203|doi:10.1039/c1gc15043j

Space GroupCrystallography6a713a14-Tetrahydro-6H13H-indolo[1'2':45]pyrazino[12-a]indole-613-dioneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
researchProduct

CCDC 262066: Experimental Crystal Structure Determination

2006

Related Article: G.Stajer, A.E.Szabo, G.Turos, P.Sohar, R.Sillanpaa|2005|Eur.J.Org.Chem.|2005|4154|doi:10.1002/ejoc.200500155

Space GroupCrystallography811-Methano-12344a7ac8c11c11ac13a-decahydroindolo[17a-a][31]benzoxazine-612-dioneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
researchProduct

CCDC 262064: Experimental Crystal Structure Determination

2006

Related Article: G.Stajer, A.E.Szabo, G.Turos, P.Sohar, R.Sillanpaa|2005|Eur.J.Org.Chem.|2005|4154|doi:10.1002/ejoc.200500155

Space GroupCrystallography811-Methano-12344a7ac8t11t11ac13a-decahydroindolo[17a-a][31]benzoxazine-612-dioneCrystal SystemCrystal StructureCell ParametersExperimental 3D Coordinates
researchProduct