# Saul Lubkin

## Professor of Mathematics

## Courses

Mth162, Calculus IIA, CRN 30480, MW 9:00-10:15, B&L 109

Course home page for Mth162, Spring, 2018

Mth165, Linear Algebra with Differential Equations, CRN 30723, MW 2:00-3:15, HH140

Course home page for Mth165, Spring, 2018

Mth391, Independent Study, CRN 31129

## Research Interests

Algebraic Geometry

Homological Algebra

Commutative Algebra

Algebraic Topology

## Links to some useful papers

On Several Points of Homological Algebra, by Alexandre Grothendieck

Algebraic Coherent Sheaves, by Jean Pierre Serre

A well-written paper about sheaves

An addendum to Kelley's "General Topology"
written by myself that constructs the completion of a uniform space directly without using metrization theorems.

Imbedding of Abelian Categories, by Saul Lubkin: A paper that reduces proving many theorems in abelian categories to the case of the category of abelian groups.

## Current Research

The paper below constructs a $p$-adic cohomology theory on algebraic varieties in characteristic $p$, that appears to be superior to all other $p$-adic cohomology theories so far constructed (For example, for Euclidean space of dimension $n$ over a ring $A$ in characteristic $p$, it is isomorphic to EXACTLY the de Rham cohomology of Euclidean space of dimension $n$ over $W_(A)$: there is no extra torsion, and, a foriori, no topological torsion. $W_(A)$ is a subring of $W(A)$ that I call the bounded Witt vectors on $A$.). I am currently doing research to extend the results of this paper.
Generalization of p-adic cohomology; bounded Witt vectors. A canonical lifting of a variety in charecteristic p back to characteristic zero, by Saul Lubkin.