moduli problems and morphisms - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T06:56:10Z http://mathoverflow.net/feeds/question/80311 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/80311/moduli-problems-and-morphisms moduli problems and morphisms Forström 2011-11-07T15:42:24Z 2011-11-07T15:42:24Z <p>Hello,</p> <p>I'm studying the reduction of two Shimura varieties over $\overline{\mathbb{F}_p}$. I define a map on the moduli problems of these two varieties, and I would like to show that this is actually an algebraic map between algebraic varieties.</p> <p>I need to define a morphism of functors between the two moduli problems, but this seems to require an extensive use of Dieudonné module theory over any $\overline{\mathbb{F}_p}$-scheme, which is too complicated in this case. Is there any other option ?</p> <p>For example, in the proof of the Eichler-Shimura relation for modular curves, one defines sections for the two maps $X_0(p) \longrightarrow X_0$. Why are they algebraic maps ? Thank you !</p>