Cours spécialisé (TN, GA)
Exponential motives
Javier Fresan
Contact : fresan à imj-prg.fr
Pas de notes de cours prévues.
Langue du cours : Anglais
Présentation
Exponential motives are a universal cohomology theory for pairs consisting of an algebraic variety over some field and a regular function on it. These objects have attracted considerable attention in recent years, especially in connection with exponential periods, exponential sums over finite fields, and mirror symmetry for Fano varieties. At first sight unrelated, these three topics enjoy rich connections with each other. Guided by the philosophy of exponential motives, we can sometimes turn into theorems what had earlier been inspiring analogies.
Contenu
- Rapid decay cohomology, twisted de Rham cohomology, and the comparison isomorphism
- The category of perverse sheaves with vanishing cohomology on the affine line
- Construction of the tannakian category of exponential motives over a subfield of the complex numbers
- Characterisation of classical motives within the category of exponential motives
- The exponential period conjecture
- Applications to E-functions
Prérequis
Variétés algébriques, Schémas I: introduction à la théorie des schémas, Schémas II: faisceaux coherents et cohomologie.
The course "Perverse sheaves and decomposition theorem" would definitely be useful but is not a prerequisite.
Bibliographie