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Noetherianity of some degree two twisted commutative algebras

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Abstract

The resolutions of determinantal ideals exhibit a remarkable stability property: for fixed rank but growing dimension, the terms of the resolution stabilize (in an appropriate sense). One may wonder if other sequences of ideals or modules over coordinate rings of matrices exhibit similar behavior. We show that this is indeed the case. In fact, our main theorem is more fundamental in nature: It states that certain large algebraic structures (which are examples of twisted commutative algebras) are noetherian. These are important new examples of large noetherian algebraic structures, and ones that are in some ways quite different from previous examples.

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Notes

  1. One should ask that all G-equivariant coherent sheaves are noetherian, not just the structure sheaf.

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Author notes

  1. Rohit Nagpal

    Present address: Department of Mathematics, The University of Chicago, Chicago, IL, USA

  2. Steven V Sam

    Present address: Department of Mathematics, University of Wisconsin, Madison, WI, USA

Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, Madison, WI, USA

    Rohit Nagpal

  2. Department of Mathematics, University of California, Berkeley, CA, USA

    Steven V Sam

  3. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Andrew Snowden

Authors
  1. Rohit Nagpal
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  2. Steven V Sam
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  3. Andrew Snowden
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Corresponding author

Correspondence to Steven V Sam.

Additional information

S.S. was supported by a Miller research fellowship. A.S. was supported by NSF Grant DMS-1303082.

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Nagpal, R., Sam, S.V. & Snowden, A. Noetherianity of some degree two twisted commutative algebras. Sel. Math. New Ser. 22, 913–937 (2016). https://doi.org/10.1007/s00029-015-0205-y

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