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Number Theory
Collects articles from the meeting of the Canadian Number Theory Association held at the Centre de Recherches Mathematiques (CRM) at the University of Montreal. This book covers topics such as algebraic number theory, analytic number theory, arithmetic algebraic geometry, computational number theory, and Diophantine analysis and approximation.
Lectures on Hilbert Modular Varieties and Modular Forms
This book is devoted to certain aspects of the theory of $p$-adic Hilbert modular forms and moduli spaces of abelian varieties with real multiplication. The theory of $p$-adic modular forms is presented first in the elliptic case, introducing the reader to key ideas of N. M. Katz and J.-P. Serre. It is re-interpreted from a geometric point of view, which is developed to present the rudiments of a similar theory for Hilbert modular forms. The theory of moduli spaces of abelianvarieties with real multiplication is presented first very explicitly over the complex numbers. Aspects of the general theory are then exposed, in particular, local deformation theory of abelian varieties in positive characteristic. The arithmetic of $p$-adic Hilbert modular forms and the geometry ofmoduli spaces of abelian varieties are related. This relation is used to study $q$-expansions of Hilbert modular forms, on the one hand, and stratifications of moduli spaces on the other hand. The book is addressed to graduate students and non-experts. It attempts to provide the necessary background to all concepts exposed in it. It may serve as a textbook for an advanced graduate course.
Hilbert Modular Forms: mod $p$ and $p$-Adic Aspects
We study Hilbert modular forms in characteristic $p$ and over $p$-adic rings. In the characteristic $p$ theory we describe the kernel and image of the $q$-expansion map and prove the existence of filtration for Hilbert modular forms; we define operators $U$, $V$ and $\Theta_\chi$ and study the variation of the filtration under these operators. Our methods are geometric - comparing holomorphic Hilbert modular forms with rational functions on a moduli scheme with level-$p$ structure, whose poles are supported on the non-ordinary locus.In the $p$-adic theory we study congruences between Hilbert modular forms. This applies to the study of congruences between special values of zeta functions of totally real fields. It also allows us to define $p$-adic Hilbert modular forms 'a la Serre' as $p$-adic uniform limit of classical modular forms, and compare them with $p$-adic modular forms 'a la Katz' that are regular functions on a certain formal moduli scheme. We show that the two notions agree for cusp forms and for a suitable class of weights containing all the classical ones. We extend the operators $V$ and $\Theta_\chi$ to the $p$-adic setting.
Hollow Land
How does Israel extend its control over Palestinian lands? From the tunnels of Gaza to the militarized airspace of the Occupied Territories, Eyal Weizman unravels the mechanisms of control and how they have transformed Gaza and the West Bank into a war zone. This is essential reading for understanding how architecture and infrastructure are used as lethal weapons in the formation of Israel. In this new edition, Weizman explains how the events following the invasion of Gaza in October 2023 bear witness to the continuing policies of oppression. He details how this book became a foundational text for Forensic Architecture.
Geometric Modular Forms and Elliptic Curves
1. An algebro-geometric tool box. 1.1. Sheaves. 1.2. Schemes. 1.3. Projective schemes. 1.4. Categories and functors. 1.5. Applications of the key-lemma. 1.6. Group schemes. 1.7. Cartier duality. 1.8. Quotients by a group scheme. 1.9. Morphisms. 1.10. Cohomology of coherent sheaves. 1.11. Descent. 1.12. Barsotti-Tate groups. 1.13. Formal scheme -- 2. Elliptic curves. 2.1. Curves and divisors. 2.2. Elliptic curves. 2.3. Geometric modular forms of level 1. 2.4. Elliptic curves over C. 2.5. Elliptic curves over p-adic fields. 2.6. Level structures. 2.7. L-functions of elliptic curves. 2.8. Regularity. 2.9. p-ordinary moduli problems. 2.10. Deformation of elliptic curves -- 3. Geometric modular forms. 3.1. Integrality. 3.2. Vertical control theorem. 3.3. Action of GL(2) on modular forms -- 4. Jacobians and Galois representations. 4.1. Jacobians of stable curves. 4.2. Modular Galois representations. 4.3. Fullness of big Galois representations -- 5. Modularity problems. 5.1. Induced and extended Galois representations. 5.2. Some other solutions. 5.3. Modularity of Abelian Q-varieties
Divine Service?
Religion now plays an increasingly prominent role in the discourse on international security. Within that context, attention largely focuses on the impact exerted by teachings rooted in Christianity and Islam. By comparison, the linkages between Judaism and the resort to armed force are invariably overlooked. This book offers a corrective. Comprising a series of essays written over the past two decades by one of Israel's most distinguished military sociologists, its point of departure is that the establishment of the state of Israel in 1948, quite apart from revolutionizing Jewish political activity, also triggered a transformation in Jewish military perceptions and conduct. Soldiering, whic...
Gifts from Jerusalem Jews to the Austro-Hungarian Monarchs
Presentations of offerings to the emperor-king on anniversaries of his accession became an important imperial ritual in the court of Franz Joseph I. This book explores for the first time the identity constructions of Orthodox Jewish communities in Jerusalem as expressed in their gifts to the Austro-Hungarian Kaisers at the time of dramatic events. It reveals how the beautiful gifts, their dedications, and their narratives, were perceived by gift-givers and recipients as instruments capable of acting upon various social, cultural and political processes. Lily Arad describes in a captivating manner the historical narratives of the creation and presentation of these gifts. She analyzes the iconography of these gifts as having transformative effect on the self-identification of the Jewish communities and examines their reception by the Kaisers and in the Austrian and the Palestinian Jewish press. This groundbreaking book unveils Jewish cultural and political strategies aimed to create local Eretz-Israel identities, demonstrating distinct positive communal identification which at times expressed national sentiments and at the same time preserved European identification.
Diophantine Geometry
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
