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Michael D. Fried

  1. Moduli of relatively nilpotent extensions.

    Пт, 10/23/2009 - 14:26 — SomNambul
    Authors: Michael D. Fried
    Subjects: Number Theory
    Abstract

    Gives the most precise available description of the p-Frattini module for any
    p-perfect finite group G=G0 (Thm. 2.8), and therefore of the groups G_{k,ab}, k
    \ge 0, from which we form the abelianized M(odular) T(ower). \S 4 includes a
    classification of Schur multiplier quotients, from which we figure two points
    (see the html file this http URL):

    1. Whether there is a non-empty MT over a given Hurwitz space component at
    level 0; and

    2. whether all cusps above a given level 0 o-p' cusp are p-cusps.

  2. Relating two genus 0 problems of John Thompson.

    Пт, 10/23/2009 - 04:10 — SomNambul
    Authors: Michael D. Fried
    Subjects: Algebraic Geometry
    Abstract

    The "relating" entwines three problems:

    1. Davenport's Problem, describing pairs of polynomials over Q whose ranges
    on Z/p are the same for almost all p.

    2. Showing that the monodromy groups of rational function maps over the
    complexes are limited to a finite set of groups, outside of groups close to
    alternating groups (example, symmetric groups) with special representations,
    and dihedral and cyclic groups.

  3. The place of exceptional covers among all diophantine relations.

    Втр, 10/20/2009 - 12:53 — SomNambul
    Authors: Michael D. Fried
    Subjects: Number Theory
    Abstract

    A cover of normal varieties is exceptional over a finite field if the map on
    points over infinitely many extensions of the field is one-one. A cover over a
    number field is exceptional if it is exceptional over infinitely many residue
    class fields. The first result: The category of exceptional covers of a normal
    variety, Z, over a finite field, F_q, has fiber products, and therefore a
    natural Galois group (with permutation representation) limit. This has many
    applications to considering Poincare series attached to diophantine questions.
    The paper follows three lines:

  4. The place of exceptional covers among all diophantine relations.

    Втр, 10/20/2009 - 12:53 — SomNambul
    Authors: Michael D. Fried
    Subjects: Number Theory
    Abstract

    A cover of normal varieties is exceptional over a finite field if the map on
    points over infinitely many extensions of the field is one-one. A cover over a
    number field is exceptional if it is exceptional over infinitely many residue
    class fields. The first result: The category of exceptional covers of a normal
    variety, Z, over a finite field, F_q, has fiber products, and therefore a
    natural Galois group (with permutation representation) limit. This has many
    applications to considering Poincare series attached to diophantine questions.
    The paper follows three lines:

Math-arch

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