Séminaire de Mathématique

Vologodsky and Coleman integration on curves with semi-stable reduction

by Prof. Amnon BESSER (Ben Gurion University & IHÉS)

Amphitéâtre Léon Motchane (IHES)

Amphitéâtre Léon Motchane


Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Coleman and Vologodsky integration theories give canonical parallel transports for unipotent differential equations - Coleman on overconvergent spaces with good reduction and Vologodsky on algebraic varieties, both over p-adic fields. In Coleman's theory the transport is via a path invariant under the action of Frobenius while in Vologodsky's theory one adds a condition involving the monodromy operator. While both theories can be formulated in fairly similar terms, the precise relationship between them is a bit unclear. In this talk, based on joint work in progress with Sarah Zerbes, I will describe some background on the two integration theories and I will describe the simplest non-trivial case - a holomorphic form on a curve with semi-stable reduction, where we can say what the relation should be. Time permitting I'll discuss possible applications to syntomic regulators.