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16 Jul 2018: Profinite Properties of 3-ManifoldGroups. Gareth Wilkes. St John’s College. University of Oxford. A thesis submitted for the degree of. Doctor of Philosophy. Trinity 2018. Dedicated to my family. Acknowledgements. Firstly I give great thanks to

18 Nov 2022: ρ,p : Gal(Q/Q) GL2(Qp). characterised by the requirement that the number τ(l) (for a prime numberl 6= p) appear as the trace, under ρ,p, of a ... Inthis case the inertia group Il acts trivially and ρE,p(σl) is an endomorphismof VpE, so might be

4 Apr 2019: Pr (α). We claim that the elementγ = β/α satisfies the requirements of the lemma.

21 Jun 2002: However it follows fromwork of Buchsbaum and Eisenbud [5] that the quadrics defining an ellipticnormal quintic may be written as the 44 Pfaffians of a 55 skew-symmetricmatrix with entries linear ... Proof. The projective representation ω is defined by

30 Mar 2022: Graded Lie Algebras, Compactified Jacobians and ArithmeticStatistics. Jef Laga. March 30, 2022. Abstract. A simply laced Dynkin diagram gives rise to a family of curves over Q and a coregular representation,using deformations of simple singularities

15 Oct 2021: MA4K5: Introduction to Mathematical Relativity. Dr. Claude Warnick. November 11, 2017. Abstract. One of the crowning achievements of modern physics is Einstein’s theory ofgeneral relativity, which describes the gravitational field to a very high

10 Mar 2015: c Copyright. Not for distribution outside Cambridge University. CONTENTS. 1: INTRODUCTION 11.1 Information 11.2 Requirements 21.3 Recommended Books 21.4 Example sheets 2. ... 1.2 Requirements. We will need to use a small amount from a number of earlier

16 Apr 2014: Automorphy lifting for residually reducible l-adic Galois. representations. Jack A. Thorne. April 16, 2014. Abstract. We prove automorphy lifting theorems for residually reducible Galois representations in the settingof unitary groups over CM fields.

1 Feb 2023: Geometric inverse problems. with emphasis on two dimensions. Gabriel P. Paternain, Mikko Salo, Gunther Uhlmann. iii. To our families and all who have supported us. This material has been published by Cambridge University Press & Assessment

24 May 2022: A Tutorial on (mainly countable) Ordinals. Thomas Forster. May 22, 2022. 2. Contents. 1 The Emergence of Ordinals: Basics 71.1 Cantor’s Discovery of Ordinals. 71.2 Ordinals as Order Types. 10. 1.2.1 Wellfoundedness. 101.3 Operations on ordinals