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

Yanhong Yang

Title:
Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
Author(s):
Yang, Yanhong
Thesis Advisor(s):
de Jong, Aise Johan
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
Abstract:
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].
Subject(s):
Mathematics
Item views
692
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Suggested Citation:
Yanhong Yang, , Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles, Columbia University Academic Commons, .

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