Transcendence in Positive Characteristic
نویسندگان
چکیده
1. Table of symbols 2 2. Transcendence for Drinfeld modules 2 2.1. Wade’s results 2 2.2. Drinfeld modules 3 2.3. The Weierstraß-Drinfeld correspondence 3 2.4. Carlitz 5 2.5. Yu’s work 6 3. t-Modules 7 3.1. Definitions 7 3.2. Yu’s sub-t-module theorem 8 3.3. Yu’s version of Baker’s theorem 8 3.4. Proof of Baker-Yu 8 3.5. Quasi-periodic functions 9 3.6. Derivatives and linear independence 12 3.7. Minimal extensions of t-modules by Ga 13 4. The “ABP-criterion” 14 4.1. Algebraic curves and functions 14 4.2. “The two t’s” 15 4.3. The function Ω(t) 16 4.4. The ABP-criterion 18 5. Difference equations 20 5.1. Difference equations and their solutions 20 5.2. The Carlitz period and Ω(t) 22 5.3. Carlitz logarithms 22 5.4. Carlitz polylogarithms and zeta values 23 5.5. Drinfeld modules of rank r ≥ 2 26 5.6. Gamma values 27 6. t-Motives 28 6.1. Anderson t-motives 28 6.2. t-Motive examples 29 6.3. Rigid Analytic Triviality 30 7. Difference Galois groups and algebraic independence 31 7.1. Galois group construction 31 7.2. Connections with t-motives 33
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