Academic Commons

Theses Doctoral

Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles

Yang, Yanhong

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].



  • thumnail for Yang_columbia_0054D_11316.pdf Yang_columbia_0054D_11316.pdf application/pdf 538 KB Download File

More About This Work

Academic Units
Thesis Advisors
de Jong, Aise Johan
Ph.D., Columbia University
Published Here
May 15, 2013
Academic Commons provides global access to research and scholarship produced at Columbia University, Barnard College, Teachers College, Union Theological Seminary and Jewish Theological Seminary. Academic Commons is managed by the Columbia University Libraries.