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伽罗瓦理论话题

ISBN：9781568814124，出版年：2016，中图分类号：O15 被引 599次

This book is based on a course given by the author at Harvard University in the fall semester of 1988. The course focused on the inverse problem of Galois Theory: the construction of field extensions having a given finite group as Galois group. In the first part of the book, classical methods and results, such as the Scholz and Reichardt construction for p-groups, p != 2, as well as Hilbert's irreducibility theorem and the large sieve inequality, are presented. The second half is devoted to rationality and rigidity criteria and their application in realizing certain groups as Galois groups of regular extensions of Q(T). While proofs are not carried out in full detail, the book contains a number of examples, exercises, and open problems.

Fundamental theorem of Galois theory Inverse Galois problem Embedding problem Galois group Differential Galois theory Galois cohomology Galois extension Galois module Algebra Pure mathematics Mathematics

Alesia 52 BC -- The final struggle for Gaul

公元前52年的阿莱西亚：高卢的最后斗争

Bloomsbury Publishing Nic Fields

ISBN：9781782009221，出版年：2014，中图分类号：K5

In 52 BC Caesar's continued strategy of annihilation had engendered a spirit of desperation, which detonated into a revolt of Gallic tribes under the leadership of the charismatic young Arvernian noble Vercingetorix. Major engagements were fought at Noviodunum, Avaricum, and Gergovia, with the last action being the most serious reverse that Caesar faced in the whole of the Gallic War. However, Vercingetorix soon realized that he was unable to match the Romans in pitched battle. Taking advantage of the tribesmen's superior knowledge of their home territory, Vercingetorix began a canny policy of small war and defensive manoeuvres, which gravely hampered Caesar's movements by cutting off his supplies. For Caesar it was to be a grim summertime – his whole Gallic enterprise faced disaster. In the event, by brilliant leadership, force of arms, and occasionally sheer luck, Caesar succeeded in stamping out the revolt in a long and brutal action culminating in the siege of Alesia. Vercingetorix finally surrendered and Alesia was to be the last significant resistance to the Roman will. Never again would a Gallic warlord independent of Rome hold sway over the Celts of Gaul.

Guerrilla warfare Azorella selago Argon–argon dating Galvanic anode Gibberella xylarioides Apocalypse of Abraham Inverse Galois problem Alpha decay Horatio Alger myth Galilean invariance