Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
By: Yanhong Yang
Publisher: [publisher not identified]
Published: 2013
Place of publication: [New York, N.Y.?]
Language: eng
Description: 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].
Notes: Department: Mathematics.

Thesis advisor: Aise Johan de Jong.

Thesis (Ph.D.)--Columbia University, 2013.