Recovering divisor classes via their (T)-adic filtrations

Claudia Miller

doi:10.1016/S0022-4049(96)00182-X

Recovering divisor classes via their (T)-adic filtrations

Claudia Miller

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Continuing the investigation of the canonical map of divisor class groups j* : C1(B) → C1(B/tB), we consider what happens if ker j* is nonzero. The first result gives an injection of C1(B) into Π_n≥1 C1(B/tⁿB), where the definition of class group is extended to include the rings B/tⁿB. We also get an action of ker j* on small MCM B-modules, resulting, in the case of a ring A without DCG and with a small MCM module C, in infinitely many distinct small MCM A[[T]]-modules lifting C.

Original language	English (US)
Pages (from-to)	257-271
Number of pages	15
Journal	Journal of Pure and Applied Algebra
Volume	127
Issue number	3
DOIs	https://doi.org/10.1016/S0022-4049(96)00182-X
State	Published - May 29 1998
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/S0022-4049(96)00182-X

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abstract = "Continuing the investigation of the canonical map of divisor class groups j* : C1(B) → C1(B/tB), we consider what happens if ker j* is nonzero. The first result gives an injection of C1(B) into Πn≥1 C1(B/tnB), where the definition of class group is extended to include the rings B/tnB. We also get an action of ker j* on small MCM B-modules, resulting, in the case of a ring A without DCG and with a small MCM module C, in infinitely many distinct small MCM A[[T]]-modules lifting C.",

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AB - Continuing the investigation of the canonical map of divisor class groups j* : C1(B) → C1(B/tB), we consider what happens if ker j* is nonzero. The first result gives an injection of C1(B) into Πn≥1 C1(B/tnB), where the definition of class group is extended to include the rings B/tnB. We also get an action of ker j* on small MCM B-modules, resulting, in the case of a ring A without DCG and with a small MCM module C, in infinitely many distinct small MCM A[[T]]-modules lifting C.

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Recovering divisor classes via their (T)-adic filtrations

Abstract

ASJC Scopus subject areas

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