Support varieties: an ideal approach

By Aslak Bakke Buan, Henning Krause, Oyvind Solberg. 2005

77 citations recorded by the source corpus.

We define support varieties in an axiomatic setting using the prime spectrum of a lattice of ideals. A key observation is the functoriality of the spectrum and that this functor admits an adjoint. We assign to each ideal its support and can classify ideals in terms of their support. Applications arise from studying abelian or triangulated tensor categories. Specific examples from algebraic geometry and modular representation theory are discussed, illustrating the power of this approach which is inspired by recent work of Balmer.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8f50f886d89e6e9e3444cc707093a19e8137fb6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Tensor categorical foundations of algebraic geometry (2014, methodology): “Balmer’s result has been generalized to quasi-compact quasi-separated schemes by Buan, Krause and Solberg ([BKS07]).”
Support theory via actions of tensor triangulated categories (2011, background): “Recall from [17] that Spc T c is spectral in the sense of Hochster [25] and we have assumed it is also noetherian.”
Classifying thick subcategories of the stable category of Cohen-Macaulay modules (2009, unknown): “For example, see [7, 8, 9, 43, 15, 11, 38, 13, 20, 53].”
Supports and filtrations in algebraic geometry and modular representation theory (2007, background): “Buan, Krause and Solberg recently gave the above generalization in [ 5 ].,As already mentioned, the reader will find in [ 5 ] the extension of this result to X quasi-compact and quasi-separated (i.e.”
Spectra, spectra, spectra – Tensor triangular spectra versus Zariski spectra of endomorphism rings (2010, methodology): “Using preexisting classifications of thick ̋–ideals, some triangular spectra have been computed in [1; 9]: In algebraic geometry, the spectrum of the derived category of perfect complexes KDDperf.”