Lim Ulrich sequences and Lech’s conjecture

نویسندگان

چکیده

The long standing Lech’s conjecture in commutative algebra states that for a flat local extension $$(R,\mathfrak {m})\rightarrow (S,\mathfrak {n})$$ of Noetherian rings, we have an inequality on the Hilbert–Samuel multiplicities: $$e(R)\le e(S)$$ . In general is wide open when $$\dim R>3$$ , even equal characteristic. this paper, prove all dimensions, provided {m})$$ standard graded ring over perfect field localized at homogeneous maximal ideal. We introduce notions lim Ulrich and weakly sequences. Roughly speaking these are sequences finitely generated modules not necessarily Cohen–Macaulay, but asymptotically behave like modules. existence imply conjecture. Though known very limited cases, construct domains fields positive

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ژورنال

عنوان ژورنال: Inventiones Mathematicae

سال: 2022

ISSN: ['0020-9910', '1432-1297']

DOI: https://doi.org/10.1007/s00222-022-01149-2