Ravi Ramakrishna, tell me about Wild and Tame Galois groups !
DMA Salle WAbsolute Galois groups have played a central role in most major breakthroughs in Algebraic Number Theory in the last half century. Typically the action of these groups is through an "almost pro-p quotient" with ramification at primes above p. For such groups the Poitou-Tate duality theorems are powerful. These theorems do not hold for pro-p groups unramified at primes above p. I will survey how this tame situation differs from the wild one above and introduce theorems of Labute and Schmidt which give situations where certain tame Galois groups have […]