We give formulas for the genera of all the possible quotient of a Fermat curve by a group of automorphisms in characteristic zero and for many classes of quotient curves also in positive characteristic. We use those results for giving evidence to the conjecture that, in any fixed positive characteristic, there should exist supersingular curves for any genus. © 2009 Elsevier Inc. All rights reserved.
Supersingular quotients of Fermat curves
Re, Riccardo
2009
Abstract
We give formulas for the genera of all the possible quotient of a Fermat curve by a group of automorphisms in characteristic zero and for many classes of quotient curves also in positive characteristic. We use those results for giving evidence to the conjecture that, in any fixed positive characteristic, there should exist supersingular curves for any genus. © 2009 Elsevier Inc. All rights reserved.
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