Zipping Tate resolutions and exterior coalgebras

Fløystad, Gunnar

doi:10.1016/j.jalgebra.2015.04.007

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Question 611 What Can One Say About the Cone Of Cohomology1

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2016

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“…Eisenbud and Schreyer [ES3] generalize the theorem above to coherent sheaves, but have to allow infinite decompositions, and cannot even guarantee rational coefficients. Fløystad [Fl2] conjectures what the cohomology tables of coherent sheaves should be if regularity conditions on a coherent sheaf F and its derived dual are specified.…”

Section: Question 611 What Can One Say About the Cone Of Cohomologymentioning

confidence: 99%

Three themes of syzygies

Fløystad

McCullough

Peeva

2016

Bull. Amer. Math. Soc.

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Abstract. We present three exciting themes of syzygies, where major progress has been made recently: Boij-Söderberg theory, Stillman's question, and syzygies over complete intersections.Free resolutions are both central objects and fruitful tools in commutative algebra. They have many applications in algebraic geometry, computational algebra, invariant theory, hyperplane arrangements, mathematical physics, number theory, and other fields. We introduce and motivate free resolutions and their invariants in Sections 1 and 3. The other sections focus on three hot topics, where major progress has been made recently:• Syzygies over complete intersections (see Section 2), • Stillman's question (see Section 4), • Boij-Söderberg theory (see Sections 5 and 6).Of course, there are a number of other interesting aspects of syzygies. The expository papers [MP, PS] contain many open problems and conjectures.

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Section: Question 611 What Can One Say About the Cone Of Cohomologymentioning

confidence: 99%