For more information about this meeting, contact Robert Vaughan, Mihran Papikian, Ae Ja Yee, Kirsten Eisentraeger.

Title: | Descent for specializations of Galois branched covers |

Seminar: | Algebra and Number Theory Seminar |

Speaker: | Ryan Eberhart, Penn State University |

Abstract: |

Let G be a finite group and K a number field. Hilbert's irreducibility theorem states that a regular G-Galois branched cover of P^1_K, the projective line over K, gives rise to G-Galois field extensions of K by specializing the cover (i.e. plugging in specific coordinates into the equations for the cover). A common tactic for progress on the Inverse Galois Problem over Q is to construct a G-Galois branched cover of P^1_Q. We investigate a related line of inquiry: given a G-Galois branched of P^1_K, do any of the specializations descend to a G-Galois field extension of Q, even though the cover itself may not? We prove that the answer is yes when G is cyclic if one allows specializations at closed points. However, we show that the answer is in general no if we restrict to specializations at K-rational points. This is joint work with Hilaf Hasson. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 01 / 29 / 2015 |

Time: | 11:15am - 12:05pm |