2015/07/03 by Stäbler, Axel
#14F10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13A35 #Secondary 14B05
paper · doi:10.48550/arxiv.1507.00944
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 → 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.