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algebra / Commutative algebra; graded Betti numbers and syzygies

The lex-plus-powers conjecture over fields of characteristic zero

Claims the lex-plus-powers conjecture over every characteristic-zero field, for regular sequences of any length with degrees at least two and no growth condition, with no restriction on the other generators of II; this contains the Eisenbud-Green-Harris statement. The key new step is a Hilbert-matching monomial ideal with no smaller Betti numbers (Mermin-Murai Conjecture 10.2). It does NOT treat positive characteristic.

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algebraSep 23, 2026Significance 36/100Registry: unreviewed

The lex-plus-powers conjecture over fields of characteristic zero

Prior state unknown→proved

Claims the lex-plus-powers conjecture over every characteristic-zero field, for regular sequences of any length with degrees at least two and no growth condition, with no restriction on the other generators of II; this contains the Eisenbud-Green-Harris statement. The key new step is a Hilbert-matching monomial ideal with no smaller Betti numbers (Mermin-Murai Conjecture 10.2). It does NOT treat positive characteri…

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Claims the lex-plus-powers conjecture over every characteristic-zero field, for regular sequences of any length with degrees at least two and no growth condition, with no restriction on the other generators of II; this contains the Eisenbud-Green-Harris statement. The key new step is a Hilbert-matching monomial ideal with no smaller Betti numbers (Mermin-Murai Conjecture 10.2). It does NOT treat positive characteristic.

Claims the lex-plus-powers conjecture over every characteristic-zero field, for regular sequences of any length with degrees at least two and no growth condition, with no restriction on the other generators of II; this contains the Eisenbud-Green-Harris statement. The key new step is a Hilbert-matching monomial ideal with no smaller Betti numbers (Mermin-Murai Conjecture 10.2). It does NOT treat positive characteristic.

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