ON A QUESTION OF KEATING AND RUDNICK Introduction We ...

• exposé

ON A QUESTION OF KEATING AND RUDNICK NICHOLAS M. KATZ Introduction We work over a finite field k = Fq inside a fixed algebraic closure k. We fix a squarefree monic polynomial f(X) ∈ k[X] of degree n ≥ 2. We form the k-algebra B := k[X]/(f(X)), which is finite etale over k of degree n. We denote by u ∈ B the image of X in B under the “reduction mod f” homomorphism k[X] → B. Thus we may write this homomorphism as g(X) ∈ k[X]

• perverse sheaf
• power frobenius endomorphism fk of b.
• finite extension field
• b×
• group h1c
• gm
• characters
• product