School of Mathematics Seminars and Lectures
Delta Geometry and Group Schemes
by Prof. Arnab Saha (IIT Gandhinagar)
Friday, December 11, 2020
from
to
(Asia/Kolkata)
Description |
Abstract: Delta geometry was initially developed by A. Buium as ananalogue of differential algebra. In this theory, a non-linear operator \delta with respect to a non-zero prime \mathfrak{p} on a fixed number ring plays the analogous role of a derivation in the case of function rings. Such a \delta comes from the ring of Witt vectors and its associated lift of Frobenius. As an example, \delta on the ring of integers \mathbb{Z} is the Fermat quotient operator given by \delta x = \frac{x-x^p}{p}. Now given a group scheme G defined over a ring with a \delta on it, for every n, one can canonically define the arithmetic jet space J^nG which is an extension of G by another group scheme N^n. In this talk, we will discuss the structure of N^n in detail. We will then look into the application of the above in p-adic Hodge theory in the case when G is an abelian scheme. |
Material: |