The Tate Resolution Over a Complete Intersection Ring

Authors

Kolton O'Neal, University of Nebraska-LincolnFollow

First Advisor

Eloísa Grifo

Second Advisor

Mark Walker

Date of this Version

Spring 3-31-2025

Document Type

Thesis

Citation

O'Neal, K. 2025. The Tate Resolution Over a Complete Intersection Ring. Undergraduate Honors Thesis. University of Nebraska-Lincoln.

Comments

Copyright Kolton O'Neal 2025.

Abstract

Given a Noetherian commutative ring R and an ideal I ⊆ R, Tate provided a construction in [5] to produce a DG R-algebra that is also a free resolution for R/I. In this work, we review free resolutions and DG algebras, describe Tate’s construction, and present a proof of a result from Tate’s paper about his construction when a regular sequence is involved. Specifically, this result is that it only takes two steps of Tate’s construction to resolve a characteristic 0 field k over k[[x1, . . . , xn]]/(f1, . . . , fc), where f1, . . . , fc is a regular sequence over k[[x1, . . . , xn]].