Purity of the stratification by Newton polygons and Frobeniusperiodic vector bundles
 Title:
 Purity of the stratification by Newton polygons and Frobeniusperiodic vector bundles
 Author(s):
 Yang, Yanhong
 Thesis Advisor(s):
 de Jong, Aise Johan
 Date:
 2013
 Type:
 Theses
 Degree:
 Ph.D., Columbia University
 Department(s):
 Mathematics
 Persistent URL:
 https://doi.org/10.7916/D8XW4S1V
 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 genus2 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
 714
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 Suggested Citation:
 Yanhong Yang, 2013, Purity of the stratification by Newton polygons and Frobeniusperiodic vector bundles, Columbia University Academic Commons, https://doi.org/10.7916/D8XW4S1V.