Abstract: Delta geometry was initially developed by A. Buium as an
analogue 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.
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