On singular supports in mixed characteristic

2025/01/14 by Saito, Takeshi
#11G25 #14F20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.07965

Abstract

We fix an excellent regular noetherian scheme S over \mathbf Z_(p) satisfying a certain finiteness condition. For a constructible étale sheaf \cal F on a regular scheme X of finite type over S, we introduce a variant of the singular support relatively to S and prove the existence of a saturated relative variant of the singular support by adopting the method of Beilinson using the Radon transform. We may deduce the existence of the singular support itself, if we admit an expected property on the micro support of tensor product and if the scheme X is sufficiently ramified over the base S.

Related

• Relative singular support and the semi-continuity of characteristic cycles for étale sheaves
• Character sheaves in characteristic p have nilpotent singular support
• Brylinski-Radon transformation in characteristic p>0
• Comparison of the two notions of characteristic cycles
• Characteristic cycles of constructible sheaves and microlocalization