Speaker: Rakesh Pawar
Affiliation: ENS Lyon
Title: Comparison of Coniveau and Postnikov spectral sequences in the motivic homotopy category
Date and Time: August 2, 2024, 16:00:00 Hours
Venue: AG-77
Asbtract: Classically, Federer (1956), Oda and Shitanda (1986) studied homotopy groups of the space of pointed maps map_*(X, Y) from a connected CW-complex X to a connected space Y. This was achieved by comparing on one hand, (skeletal/cellular) spectral sequence coming from cellular filtration on X and on the other hand the (Postnikov) spectral sequence coming from Postnikov tower of Y. Both spectral sequences conditionally converge to homotopy groups of map_*(X, Y). In the joint work with Frederic Deglise (ENS de Lyon), currently in preparation, we consider the 'motivic homotopy theory' developed by Morel-Voevodsky (1999) suitable for algebraic varieties. We study the analogue of the above-mentioned classical result in the motivic homotopy theory context. We consider an appropriate simplicial set map_*(X_+, Y) for a scheme X over a field k and Y a pointed simplicial sheaf. Motivated by the classical result mentioned above, and a similar result in Voevodsky's motivic triangulated derived category, we compare the 'coniveau' spectral sequence with the 'Postnikov' spectral sequence both converging to homotopy groups of map_*(X_+, Y), under appropriate assumptions on a smooth scheme X, a simplicial sheaf Y and the base field k.
Affiliation: ENS Lyon
Title: Comparison of Coniveau and Postnikov spectral sequences in the motivic homotopy category
Date and Time: August 2, 2024, 16:00:00 Hours
Venue: AG-77
Asbtract: Classically, Federer (1956), Oda and Shitanda (1986) studied homotopy groups of the space of pointed maps map_*(X, Y) from a connected CW-complex X to a connected space Y. This was achieved by comparing on one hand, (skeletal/cellular) spectral sequence coming from cellular filtration on X and on the other hand the (Postnikov) spectral sequence coming from Postnikov tower of Y. Both spectral sequences conditionally converge to homotopy groups of map_*(X, Y). In the joint work with Frederic Deglise (ENS de Lyon), currently in preparation, we consider the 'motivic homotopy theory' developed by Morel-Voevodsky (1999) suitable for algebraic varieties. We study the analogue of the above-mentioned classical result in the motivic homotopy theory context. We consider an appropriate simplicial set map_*(X_+, Y) for a scheme X over a field k and Y a pointed simplicial sheaf. Motivated by the classical result mentioned above, and a similar result in Voevodsky's motivic triangulated derived category, we compare the 'coniveau' spectral sequence with the 'Postnikov' spectral sequence both converging to homotopy groups of map_*(X_+, Y), under appropriate assumptions on a smooth scheme X, a simplicial sheaf Y and the base field k.