7 citations · 39 across the 13 of their papers we have counts for
19 papers
Dévissage for periodic cyclic homology of complete intersections
Michael K. Brown, Mark E. Walker
We prove that the dévissage property holds for periodic cyclic homology for a local complete intersection embedding into a smooth scheme. As a consequence, we show that the complex…
Periodicity of ideals of minors in free resolutions
Michael K. Brown, Hailong Dao, Prashanth Sridhar
We study the asymptotic behavior of the ideals of minors in minimal free resolutions over local rings. In particular, we prove that such ideals are eventually 2-periodic over compl…
A short proof of the Hanlon-Hicks-Lazarev Theorem
Michael K. Brown, Daniel Erman
We give a short, new proof of a recent result of Hanlon-Hicks-Lazarev about toric varieties. As in their work, this leads to a proof of a conjecture of Berkesch-Erman-Smith on virt…
Positivity and nonstandard graded Betti numbers
Michael K. Brown, Daniel Erman
A foundational principle in the study of modules over standard graded polynomial rings is that geometric positivity conditions imply vanishing of Betti numbers. The main goal of th…
Linear syzygies of curves in weighted projective space
Michael K. Brown, Daniel Erman
We develop analogues of Green's -conditions for subvarieties of weighted projective space, and we prove that such -conditions are satisfied for high degree embeddings of…
Idempotent completions of equivariant matrix factorization categories
Michael K. Brown, Mark E. Walker
We prove that equivariant matrix factorization categories associated to henselian local hypersurface rings are idempotent complete, generalizing a result of Dyckerhoff in the non-e…
A short resolution of the diagonal for smooth projective toric varieties of Picard rank 2
Michael K. Brown, Mahrud Sayrafi
Given a smooth projective toric variety of Picard rank 2, we resolve the diagonal sheaf on by a linear complex of length consisting of finite direct sums…
Linear strands of multigraded free resolutions
Michael K. Brown, Daniel Erman
We develop a notion of linear strands for multigraded free resolutions, and we prove a multigraded generalization of Green's Linear Syzygy Theorem.
Tate resolutions on toric varieties
Michael K. Brown, Daniel Erman
We develop an analogue of Eisenbud-Floystad-Schreyer's Tate resolutions for toric varieties. Our construction, which is given by a noncommutative analogue of a Fourier- Mukai trans…
Minimal free resolutions of differential modules
Michael K. Brown, Daniel Erman
We propose a notion of minimal free resolutions for differential modules, and we prove existence and uniqueness results for such resolutions. We also take the first steps toward st…
A proof of a conjecture of Shklyarov
Michael K. Brown, Mark E. Walker
We prove a conjecture of Shklyarov concerning the relationship between K. Saito's higher residue pairing and a certain pairing on the periodic cyclic homology of matrix factorizati…
Standard Conjecture D for matrix factorizations
Michael K. Brown, Mark E. Walker
We prove the non-commutative analogue of Grothendieck's Standard Conjecture D for the dg-category of matrix factorizations of an isolated hypersurface singularity in characteristic…
On the topological K-theory of twisted equivariant perfect complexes
Michael K. Brown, Tasos Moulinos
We construct a comparison map from the topological K-theory of the dg-category of twisted perfect complexes on certain global quotient stacks to twisted equivariant K-theory, gener…
Computing Schur complexes
Michael K. Brown, Hang Huang, Robert P. Laudone +4
We describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud.
A Chern-Weil formula for the Chern character of a perfect curved module
Michael K. Brown, Mark E. Walker
Let be a field of characteristic 0 and a curved -algebra. We obtain a Chern-Weil-type formula for the Chern character of a perfect -module taking…
Topological K-theory of Equivariant Singularity Categories
Michael K. Brown, Tobias Dyckerhoff
We study the topological K-theory spectrum of the dg singularity category associated to a weighted projective complete intersection. We calculate the topological K-theory of the dg…
Adams Operations on Matrix Factorizations
Michael K. Brown, Claudia Miller, Peder Thompson +1
We define Adams operations on matrix factorizations, and we show these operations enjoy analogues of several key properties of the Adams operations on perfect complexes with suppor…
On a Conjecture of Dao-Kurano
Michael K. Brown
We prove a special case of a conjecture of Dao-Kurano concerning the vanishing of Hochster's theta pairing. The proof uses Adams operations on both topological -theory and perfe…
Cyclic Adams Operations
Michael K. Brown, Claudia Miller, Peder Thompson +1
Let be a commutative, Noetherian ring and a closed subset. Define to be the Grothendieck group of those bounded complexes of fin…