6533b7d1fe1ef96bd125c4c2
RESEARCH PRODUCT
Functorial Test Modules
Manuel BlickleAxel Stäblersubject
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)Mathematicsdescription
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 $\tau \circ f_* \to f_* \circ \tau$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-05-31 |