School of Mathematics Seminars and Lectures
`Laumon 1-motives and motives with modulus'
by Dr. Federico Binda (University of Regensburg, Germany)
Wednesday, February 7, 2018
from
to
(Asia/Kolkata)
at TIFR, Mumbai ( AG-77 )
at TIFR, Mumbai ( AG-77 )
Description |
Abstract: In 1974, Deligne introduced the category $\mathcal{M}_{1}$ of 1-motives (built out of semi-abelian varieties and lattices) as algebraic analogue of the category of mixed Hodge structures of level $\leq 1$. Today, thanks to the works of Ayoub, Barbieri-Viale, Kahn, Orgogozo and Voevodsky, we know that the derived category $D^b(\mathcal{M}_{1, \mathbb{Q}})$ can be embedded as a full subcategory of $\mathbf{DM}^{eff}_{gm}(k)\otimes \mathbb{Q}$, and that this embedding admits a left adjoint, the so-called ``motivic Albanese functor''. Deligne's original definition was later generalised by Laumon, introducing what are now known as ``Laumon 1-motives'', to include in the picture all commutative connected group schemes (rather then only semi-abelian varieties). Due to the presence of unipotent groups (such as $\mathbb{G}_a$), the derived category of this bigger category cannot be realised as a full subcategory of Voevodsky's motives. In this talk, we will explain how at least a piece of this category (the ``\'etale part'') can be embedded in the bigger motivic category $\mathbf{MDM}^{eff}(k)$ of ``motives with modulus'', recently introduced by Kahn-Saito-Yamazaki, and that this embedding also admits a left adjoint (a generalized motivic Albanese functor). This is a joint work with Shuji Saito. |
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