2013 Theses Doctoral

# 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].

## Subjects

## Files

- Yang_columbia_0054D_11316.pdf application/pdf 538 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- de Jong, Aise Johan
- Degree
- Ph.D., Columbia University
- Published Here
- May 15, 2013