Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Whitehead Theorem for Nilpotent Motivic Spaces
Speaker: Biman Roy, TIFR, Mumbai
Date: April 7, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In algebraic topology, a classical result due to Whitehead states that if f : X → Y is a continuous map between simply connected CW complexes which is a homology equivalence, then f is a weak equivalence. Later Dror introduced nilpotent spaces and generalised the Whitehead theorem for nilpotent spaces. In motivic homotopy theory, A 1 -homology, introduced by F. Morel, plays the role of singular homology. Whitehead theorem holds in motivic homotopy theory also (known as A 1 -Whitehead theorem), due to Wickelgren-Williams, Shimizu. In https://doi.org/10.1112/S0010437X22007321, Asok-Fasel-Hopkins introduced nilpotent spaces in motivic homotopy theory and in arXiv:2210.05933v3, Asok-Bachmann-Hopkins generalised the A 1 -Whitehead theorem for nilpotent motivic spaces. In this talk, I will give a outline of their proof following arXiv:2210.05933v3.
Title of Talk: Whitehead Theorem for Nilpotent Motivic Spaces
Speaker: Biman Roy, TIFR, Mumbai
Date: April 7, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: In algebraic topology, a classical result due to Whitehead states that if f : X → Y is a continuous map between simply connected CW complexes which is a homology equivalence, then f is a weak equivalence. Later Dror introduced nilpotent spaces and generalised the Whitehead theorem for nilpotent spaces. In motivic homotopy theory, A 1 -homology, introduced by F. Morel, plays the role of singular homology. Whitehead theorem holds in motivic homotopy theory also (known as A 1 -Whitehead theorem), due to Wickelgren-Williams, Shimizu. In https://doi.org/10.1112/S0010437X22007321, Asok-Fasel-Hopkins introduced nilpotent spaces in motivic homotopy theory and in arXiv:2210.05933v3, Asok-Bachmann-Hopkins generalised the A 1 -Whitehead theorem for nilpotent motivic spaces. In this talk, I will give a outline of their proof following arXiv:2210.05933v3.