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Test module filtrations for unit $F$-modules

Axel Stäbler

subject

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

description

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.

yearjournalcountryeditionlanguage
2015-07-03
http://arxiv.org/abs/1507.00944