Introductory notes on valuation rings and function fields in one variable
, 2014 The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their ...
Zannier, Umberto, Scognamillo, Renata
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Counting and Averaging Problems in Graph Theory [PDF]
, 2010 Paul Gunther (1966), proved the following result: Given a continuous function f on a compact surface M of constant curvature -1 and its periodic lift g to the universal covering, the hyperbolic plane, then the averages of the lift g over increasing ...
DOUMA, FEMKE
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The Arithmetic of Elliptic and Hyperelliptic Curves with Applications to Pairing-Based Cryptography [PDF]
, 2009 After giving an extensive treatment of the theory of algebraic curves and their connection to the theory of algebraic function fields of one variable, the thesis concentrates on pairings (such as the Tate pairing) defined on groups related to a given ...
Peter, Andreas
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A note on some Picard curves over finite fields
, 2015 In this note we provide a complete classification for the Newton polygon of the Picard curvesy3=x4-xandy3=x4-1 defined over a finite field of characteristic p>3. In fact, we complete the results obtained in [19].
Tafazolian, Saeed, Kazemifard, Ahmad
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On Drinfeld modules with Rasmussen-Tamagawa type conditions: a resume (Algebraic Number Theory and Related Topics 2017) [PDF]
, 2020 Algebraic Number Theory and Related Topics 2017. December 4-8, 2017. edited by Hiroshi Tsunogai, Takao Yamazaki and Yasushi Mizusawa. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.This is an announcement of
Okumura, Yoshiaki
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Some cases of Vojta's conjecture for integral points over function fields
, 2007 In the present paper we solve, in particular, the function field version of a special case of Vojta's conjecture for integral points, namely for the variety obtained by removing a conic and two lines from the projective plane.
Umberto Zannier +3 more
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Higher derivative terms and their influence on N=2 supersymmetric systems [PDF]
, 1999 This thesis is concerned with so-called higher derivative terms which arise in low energy approximations to certain physical models. In particular, the aim is to investigate the role that such terms play in low energy N=2 supersymmetric gauge theories in
Weir, W.A., Weir, William Alexander
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Quadratic forms and related structures over fields
, 2019 : The range of topics discussed at the workshop \u201cQuadratic Forms and Related Structures over Fields\u201d included core themes from the algebraic theory of quadratic and hermitian forms and their Witt groups, several aspects of the theory of linear ...
Hoffmann, Detlev +2 more
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Class field theory in characteristic p, its origin and development
, 1998 Today’s notion of “global field ” comprises number fields (algebraic, of finite degree) and function fields (algebraic, of dimension 1, finite base field). They have many similar arithmetic properties.
Peter Roquette
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Compatible systems of Galois representations of global function fields
, 2018 Let $K$ be a finitely generated infinite field over the finite prime field $\mathbb{F}_p$ with separable closure $K^s$ and let $X$ be a smooth projective variety over $K$.
Boeckle, Gebhard
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