Proves existence of positive-density hypersurfaces over finite fields intersecting a reduced equidimensional quasiprojective scheme X such that multiplicity e_P is preserved at all closed points P of the intersection.
Algebra Number Theory
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Bertini theorems for Hilbert-Samuel multiplicity over finite fields
Proves existence of positive-density hypersurfaces over finite fields intersecting a reduced equidimensional quasiprojective scheme X such that multiplicity e_P is preserved at all closed points P of the intersection.