Algebra Seminar, Fall 2018
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Date 
Speaker 
Title/Abstract 
9/7 
Lance Miller (UArk) 
The de RhamWitt complex and the htopology
In this series of talks, we will discuss differential forms on singular schemes. Usually, one must impose some condition to make discussions fruitful, for example to consider normal schemes. We will first survey work of Huber and Joerder, and following work of Huber, Kebekus, and Kelly on how to unify many different perspectives on differential forms using Voevodsky's htopology. We then apply these ideas to Illusie's de RhamWitt complex which is joint work with V. Ertl.

9/14 
Lance Miller (UArk) 
The de RhamWitt complex and the htopology
Continuation of last week's talk.

9/21 
Paolo Mantero (UArk) 
Properties of Reeslike algebras
Reeslike algebras have been used by McCullough and Peeva to construct counterexamples to the more general statement of the EisenbudGoto regularity conjecture. In this talk, we will explore some of their algebraic and geometric properties and illustrate some structural results. This talk is based on joint work with J. McCullough and L. E. Miller.

10/5 
Paolo Mantero (UArk) 
TBA
TBA

10/10 
Alex Buium (UNM) 
Lie invariance of Frobenius lifts
We show that the padic completion of any affine elliptic curve with ordinary reduction
possesses Frobenius lifts whose "normalized" action on 1forms preserves mod p the space of invariant 1forms. We also show that, after removing the 2torsion sections,
the above situation can be "infinitesimally deformed" in the sense that
the above mod p result has a mod p^2 analogue. Finally we show that the mod p result
fails for linear algebraic groups that are not tori.
