Finite abelian covers in positive characteristics

uga
cnrs
demailly2024
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
grneoble
abelian covers

Ramified Galois covers with finite abelian groups are frequently used in complex algebraic geometry, for example in the proof of vanishing theorems. They behave differently in positive characteristics, as there exists no equivariant resolution of singularities in this setting. The talk will propose a remedy to that failure, and describe a class of diagonalizable covers with applications to curves and surfaces.