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Relating the Exterior Algebra of the Conormal Module to the Tor Algebra · arXivDesk

2608.09010Aug 10, 2026

Relating the Exterior Algebra of the Conormal Module to the Tor Algebra

Desiree Martin

Abstract

For any ideal $I$ (whose projective dimension need not be finite) in a local Noetherian ring $R$ , we show that, if the conormal module $I/I^2$ has a free summand given by $F$ , the natural map from $\bigwedge F$

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For any ideal I (whose projective dimension need not be finite) in a local Noetherian ring R, we show that, if the conormal module I/I² has a free summand given by F, the natural map from F to Tor_*^R(R/I,R/I) splits as algebras. To achieve this, we use dg algebra techniques and remodel results of André and Iyengar, proving them in setting of semi-free extensions, replacing the need for semi-free Γ-extensions.

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The paper addresses: Relating the Exterior Algebra of the Conormal Module to the Tor Algebra.
For any ideal I (whose projective dimension need not be finite) in a local Noetherian ring R, we show that, if the conormal module I/I² has a free summand given by F, the natural map from F to Tor_*^R(R/I,R/I) splits as algebras.