Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
This thesis includes two parts. In the first part, we show a purity theorem for stratifications by Newton polygons coming from crystalline cohomology, which says that the family of Newton polygons over a noetherian scheme have a common break point if this is true outside a subscheme of codimension bigger than 1. The proof is similar to the proof of [dJO99, Theorem 4.1]. In the second part, we prove that for every ordinary genus-2 curve X over a finite field k of characteristic 2 with automorphism group Z/2Z × S_3, there exist SL(2,k[[s]])-representations of π_1(X) such that the image of π_1(X^-) is infinite. This result produces a family of examples similar to Laszlo's counterexample [Las01] to a question regarding the finiteness of the geometric monodromy of representations of the fundamental group [dJ01].
AC:P:20334
Academic Commons
Yang, Yanhong
Author
de Jong, Aise Johan
Thesis advisor
Columbia University. Mathematics
Originator
Theses
English
Mathematics
text
2013
eng
2017-06-08T13:54:09Z
2017-06-08T15:33:03Z
Ph.D.
2
Mathematics
Columbia University
10.7916/D8XW4S1V