The six-functor formalism for rigid analytic motives
Joseph Ayoub, Martin Gallauer, Alberto Vezzani
Abstract
Abstract We offer a systematic study of rigid analytic motives over general rigid analytic spaces, and we develop their six-functor formalism. A key ingredient is an extended proper base change theorem that we are able to justify by reducing to the case of algebraic motives. In fact, more generally, we develop a powerful technique for reducing questions about rigid analytic motives to questions about algebraic motives, which is likely to be useful in other contexts as well. We pay special attention to establishing our results without noetherianity assumptions on rigid analytic spaces. This is indeed possible using Raynaud’s approach to rigid analytic geometry.
Topics & Concepts
Formalism (music)FunctorAlgebraic numberAlgebra over a fieldPure mathematicsMathematicsAlgebraic geometry and analytic geometryMathematical analysisVisual artsArtDifferential algebraic equationDifferential equationOrdinary differential equationMusicalHomotopy and Cohomology in Algebraic TopologyAdvanced Topics in AlgebraAdvanced Differential Equations and Dynamical Systems