The field of definition of function fields and a problem in the reducibility of polynomials in two variables
Introduction Let K be a number field, O the ring of integers of K. Suppose we are given a projective curve Z, and a morphism :Z pr(C) (where pr(C) is the projective line) such that and Z are both defined over K. We denote by K(Z) the field of functions of Z defined over K, and from this data we obtain a permutation representation T of the Galois group G(K(Z)^/K(Pr(C))) (where K(Z) is the normal closure of K(Z) over K(Pr(C) ). In Section 1 we investigate (for our needs) the combinatorial and group theoretical aspects of the situation where
Relating Two Genus 0 Problems of John Thompson
Excluding a precise list of groups like alternating, symmetric, cyclic and dihedral, from 1st year algebra (§7.2.3), we expect there are only finitely many monodromy groups of primitive genus 0 covers. Denote this nearly proven genus 0 problem as Problem 0 g=0 2. We call the exceptional groups 0-sporadic. Example: Finitely many Chevalley groups are 0-sporadic. A proven result: Among polynomial 0-sporadic groups, precisely three produce covers falling in nontrivial reduced families. Each (miraculously) defines one natural genus 0 ℚ cover of the j-line. The latest Nielsen class techniques apply to these dessins d’enfant to see their subtle arithmetic and interesting cusps.
Mutiny Echoes: India, Britons, and Charles Dickens's A Tale of Two Cities
This essay asks what, if any, import the Indian ““Mutiny”” of 1857 had on A Tale of Two Cities (1859), Charles Dickens�s fictionalized account of the French Revolution. Begun shortly after the Indian uprising started, Dickens�s historical novel appears studiously to avoid any mention of events on the Indian subcontinent, even though these events preoccupied and enraged the author. Few scholars have attended to the question of A Tale of Two Cities and the ““Mutiny,”” but when they have, scholars have looked for analogies between India and Dickens�s account of the French Revolution. In this essay, by contrast, I examine A Tale of Two Cities in a larger context——of Britons9 response to the Uprising, of Dickens9s short stories and essays in Household Words in the years before the ““Mutiny”” and immediately after, of Dickens9s disenchantment with aspects of British culture, and of his need to articulate a national identity grounded in action. I argue that the events in India were the match that ignited Dickens9s already established midcentury interests in national identity, nobility, and masculine heroism. I do not wish to suggest that A Tale of Two Cities is an Indian ““Mutiny”” novel, but rather that it is a novel about the ““Making of Britons,”” an important endeavor for an author who was intensely dissatisfied with the Britain that he saw around him.