Search results for "Smooth morphism"

showing 3 items of 3 documents

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
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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
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A criterion for extending morphisms from open subsets of smooth fibrations of algebraic varieties

2021

Abstract Given a smooth morphism Y → S and a proper morphism P → S of algebraic varieties we give a sufficient condition for extending an S-morphism U → P , where U is an open subset of Y, to an S-morphism Y → P , analogous to Zariski's main theorem.

Smooth morphismPure mathematicsAlgebra and Number TheoryAlgebraic varietySmooth fibrationZariski’s main theoremFiberwise birational morphismProper morphismMathematics::Algebraic GeometryMorphismExtending a morphismMathematics::Category TheorySettore MAT/03 - GeometriaMathematicsJournal of Pure and Applied Algebra
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