Local Systems in Algebraic-Arithmetic Geometry

Esnault, Hélène

Local Systems in Algebraic-Arithmetic Geometry
  • 出版商: Springer
  • 出版日期: 2023-09-20
  • 售價: $2,560
  • 貴賓價: 9.5 折 $2,432
  • 語言: 英文
  • 頁數: 94
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303140839X
  • ISBN-13: 9783031408397

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商品描述

The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci.
This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.

商品描述(中文翻譯)

對於光滑複雜代數多構造的拓撲基本群，我們尚未完全理解。一種方法是考慮其複線性表示模共軛，也就是它的複數局部系統。一個基本問題是找出這些模空間的複數點，它們對應於幾何系統，更一般地識別具有特殊算術性質的局部系統模空間的幾何子區域。在這些問題上已經提出了深刻的猜想。本書研究了這些猜想的一些結果，特別是一些特殊區域的密度、整性和晶體性質。
這本專著提供了一個獨特而簡潔的研究領域的概述，對於希望進入這個領域的學生非常有用。它對於廣泛的研究人員都很有興趣，並且對於新手和專家都是一個有用的參考資料。

作者簡介

Hélène Esnault is an emeritus Einstein Professor at the Freie Universität Berlin. She is currently a part time Professor at the University of Copenhagen and an associate part time Professor at Harvard University. She is working in the field of algebraic and arithmetic geometry. She established bridges between the analytic and arithmetic theories comprising for example the study of vanishing theorems, of rational points over finite fields, of complex and l-adic local systems, of analytic and arithmetic crystals, of algebraic cycles. She was awarded numerous prizes, including the Cantor medal (2019), and several honorary degrees, including the one of the University of Chicago (2023) for her "vision of algebraic geometry that touches upon most of the active branches of that vast field but is nevertheless recognizable her own."

作者簡介(中文翻譯)

Hélène Esnault是柏林自由大學的名譽愛因斯坦教授。她目前是哥本哈根大學的兼職教授，也是哈佛大學的兼職副教授。她的研究領域是代數和算術幾何。她建立了分析和算術理論之間的橋樑，包括消失定理的研究、有限域上的有理點、複數和l-週期局部系統、分析和算術晶體、代數週期等。她獲得了許多獎項，包括康托獎章（2019年），以及幾個榮譽學位，包括芝加哥大學（2023年）頒發的榮譽學位，以表彰她對代數幾何的願景，該願景觸及該廣闊領域的大部分活躍分支，但仍然具有她自己的特色。

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