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Papers by Prashanth Sridhar

arXiv (Cornell University), Mar 7, 2024

A theorem of Paul Roberts ([Rob80]) states that the integral closure of a regular local ring in a... more A theorem of Paul Roberts ([Rob80]) states that the integral closure of a regular local ring in a generically abelian extension is Cohen-Macaulay, provided the characteristic of the residue field does not divide the order of the Galois group. An example of Koh in [Koh86] shows the conclusion is false in the modular case. After a modification to the statement concerning ramification over p in codimension one, we give an extension of Roberts's theorem to the modular case for unramified regular local rings in mixed characteristic when the p-torsion of the Galois group is annihilated by p.

arXiv (Cornell University), Feb 19, 2024

We give an overview of a Macaulay2 package for computing with the multigraded BGG correspondence.... more We give an overview of a Macaulay2 package for computing with the multigraded BGG correspondence. This software builds on the package BGG due to Abo-Decker-Eisenbud-Schreyer-Smith-Stillman, which concerns the standard graded BGG correspondence. In addition to implementing the multigraded BGG functors, this package includes an implementation of differential modules and their minimal free resolutions, and it contains a method for computing strongly linear strands of multigraded free resolutions.

arXiv (Cornell University), Dec 27, 2023

A landmark theorem of Orlov relates the singularity category of a graded Gorenstein algebra to th... more A landmark theorem of Orlov relates the singularity category of a graded Gorenstein algebra to the derived category of the associated noncommutative projective scheme. We generalize this theorem to the setting of differential graded algebras. As an application, we obtain new cases of the Lattice Conjecture in noncommutative Hodge theory. Notation 1.5. Throughout, k denotes a field. We will consider bigraded k-vector spaces V =

Transactions of the American Mathematical Society, Mar 3, 2023

We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits ... more We study reflexive modules over one dimensional Cohen-Macaulay rings. Our key technique exploits the concept of I-Ulrich modules.

Transactions of the American Mathematical Society, Series B

arXiv (Cornell University), Jun 1, 2023

We study the asymptotic behavior of the ideals of minors in minimal free resolutions over local r... more 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 2periodic over complete intersections and Golod rings. We also establish general results on the stable behavior of ideals of minors in any infinite minimal free resolution. These ideals have intimate connections to trace ideals and cohomology annihilators. Constraints on the stable values attained by the ideals of minors in many situations are obtained, and they can be explicitly computed in certain cases.

We study the Cohen-Macaulay property of a particular class of radical extensions of an unramified... more We study the Cohen-Macaulay property of a particular class of radical extensions of an unramified regular local ring having mixed characteristic.

arXiv: Commutative Algebra, Jan 7, 2021

Journal of Pure and Applied Algebra, Dec 1, 2021

Let S be an unramified regular local ring of mixed characteristic p ≥ 3 and S p the subring of S ... more Let S be an unramified regular local ring of mixed characteristic p ≥ 3 and S p the subring of S obtained by lifting to S the image of the Frobenius map on S/pS. Let R be the integral closure of S in a biradical extension of degree p 2 of its quotient field obtained by adjoining p-th roots of sufficiently general square free elements f, g ∈ S p. We show that R admits a birational maximal Cohen-Macaulay module. It is noted that R is not automatically Cohen-Macaulay.

We study the small and big finitistic projective, injective and flat dimensions over a non-positi... more We study the small and big finitistic projective, injective and flat dimensions over a non-positively graded commutative noetherian DG-ring A with bounded cohomology. Our main results generalize results of Bass and Raynaud-Gruson to this derived setting, showing that any bounded DG-module M of finite flat dimension satisfies proj dim A (M) ≤ dim(H 0 (A))−inf(M). We further construct DG-modules of prescribed projective dimension, and deduce that the big finitistic projective dimension satisfies the inequalities dim(H 0 (A)) − amp(A) ≤ FPD(A) ≤ dim(H 0 (A)). It is further shown that this result is optimal, in the sense that there are examples that achieve either bound. As an application, new vanishing results for the derived Hochschild (co)homology of homologically smooth algebras are deduced. Contents 5. Constructing DG-modules of prescribed projective dimension 21 6. Finitistic dimensions 25 7. Examples 29 8. Application to homologically smooth maps 31 References 32

Let S be an unramified regular local ring of mixed characteristic two and R the integral closure ... more Let S be an unramified regular local ring of mixed characteristic two and R the integral closure of S in a biquadratic extension of its quotient field obtained by adjoining roots of sufficiently general square free elements f, g ∈ S. Let S denote the subring of S obtained by lifting to S the image of the Frobenius map on S/2S. When at least one of f, g ∈ S, we characterize the Cohen Macaulayness of R and show that R admits a birational small Cohen Macaulay module. It is noted that R is not automatically Cohen Macaulay in case f, g ∈ S or if f, g / ∈ S.

Let S be an unramified regular local ring of mixed characteristic p≥ 3 and S^p the subring of S o... more Let S be an unramified regular local ring of mixed characteristic p≥ 3 and S^p the subring of S obtained by lifting to S the image of the Frobenius map on S/pS. Let R be the integral closure of S in a biradical extension of degree p^2 of its quotient field obtained by adjoining p-th roots of sufficiently general square free elements f,g∈ S^p. We show that R admits a birational maximal Cohen-Macaulay module. It is noted that R is not automatically Cohen-Macaulay.

Let S be an unramified regular local ring of mixed characteristic p ≥ 3 and S the subring of S ob... more Let S be an unramified regular local ring of mixed characteristic p ≥ 3 and S the subring of S obtained by lifting to S the image of the Frobenius map on S/pS. Let R be the integral closure of S in a biradical extension of degree p of its quotient field obtained by adjoining p-th roots of sufficiently general square free elements f, g ∈ S. We show that R admits a birational maximal Cohen-Macaulay module. It is noted that R is not automatically Cohen-Macaulay.

Existence of birational small Cohen-Macaulay modules over biquadratic extensions in mixed characteristic

Journal of Algebra