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- W2962934372 abstract "Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k . In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG - A -module M of dimension N as a free A -module, if the homology of M is nontrivial and finite dimensional as a k -vector space, then 2 r ≤ N . Here we state a stronger conjecture about varieties of square-zero upper triangular N × N matrices with entries in A . Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when N < 8 or r < 3 without any restriction on the characteristic of k . As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when N > 4 and r = 2 ." @default.
- W2962934372 created "2019-07-30" @default.
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- W2962934372 date "2019-06-01" @default.
- W2962934372 modified "2023-09-25" @default.
- W2962934372 title "Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices" @default.
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- W2962934372 doi "https://doi.org/10.1016/j.jpaa.2018.09.007" @default.
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