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Good reduction of rational maps with marked fixed point structure

Event Detail

Event Type: 
Number Theory Seminar
Thursday, January 26, 2012 - 06:00 to 07:00
Kidder 358

Speaker Info

CUNY Graduate Center

Shafarevich's theorem on good reduction of elliptic curves states that for any finite set of places S of a number field, then the subset of
the moduli space of elliptic curves with good reduction at all places not in S is non-Zariski dense.  The analogous statement for rational maps of degree d is false, and an explicit counter example for degree 2 rational maps is given.  If one rigidifies the problem by requiring two unramified fixed points and strengthens the notion of good reduction to respect this extra structure, then an appropriate analogue is in fact true: the subset of degree two rational maps with double unramified fixed point structure and that have good reduction at all places not in S is non-Zariski dense in the moduli space of such maps. This talk summarizes joint work with Clayton Petsche.