0 problems of John Thompson
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چکیده
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 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. John Thompson earlier considered another genus 0 problem: To find θfunctions uniformizing certain genus 0 (near) modular curves. We call this Problem 1 . We pose uniformization problems for j-line covers in two cases. First: From the three 0-sporadic examples of Problem 2 . Second: From finite collections of genus 0 curves with aspects of Problem 1 .
منابع مشابه
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 2 . We call the exceptional groups 0-sporadic. Example: Finitely many Chevalley groups are 0-sporadic. A proven result: Among polynomial 0-spo...
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