Idempotent relations and generalized p - ranks of curves ∗
نویسنده
چکیده
Let Y be a smooth projective irreducible curve defined over a finite field F q. We assume that G is a finite subgroup of the automorphism group of Y whose order divides q − 1. We show that relations among idempotents corresponding to the irreducible characters of subgroups H of G imply similar relations among generalized pranks of Y. We also relate this result to the realization of finite groups as Galois groups of finite unramified Galois covers of a curve over F q .
منابع مشابه
Idempotent Relations and Fundamental Groups of Curves
Let C be a smooth projective irreducible curve defined over a finite field k. Let G be a finite subgroup of Aut(C) of order prime to char(k) and M the |G|-th cyclotomic field. We show that certain idempotent relations in M [G] imply relations among arithmetic invariants of the fundamental groups of the quotient curves (C/H)×k k, where H is a subgroup of G.
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