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+34 946 567 842
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+34 946 567 842
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ismirnov@bcamath.org
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Ikerbasque profileI am a Ramón y Cajal and Ikerbasque Research Fellow at BCAM since 2022. Personal webpage.
My principal research area is local algebra; loosely speaking this means that I study singularities, as local rings, using techniques of commutative algebra. A particular way to do so is via numerical invariants, numbers that are supposed to represent an aspect of the complexity.
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The theory of F-rational signature
Smirnov, I.
; Tucker, K. (2024)
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Lower bounds on Hilbert-Kunz multiplicities and maximal F-signature
Jeffries, J.; Nakajima, Y.; Smirnov, I.; Watanabe, K.; Yoshida, K. (2022)
ABSTRACT. Hilbert–Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both invariants are equal to one and ...
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Uniform Lech's inequality
Ma, L.; Smirnov, I. (2022)
Let (R,m) be a Noetherian local ring of dimension d ≥ 2. We prove that if e(Rred) > 1, then the classical Lech’s inequality can be improved uniformly for all m-primary ideals, that is, there exists ε > 0 such that e(I) ...
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Uniform Lech's inequality
Ma, L.; Smirnov, I. (2022)
Let (R,m) be a Noetherian local ring, and let M be a finitely generated R-module of dimension d. We prove that the set [Formula presented] is bounded below by 1/d!e(R‾) where R‾=R/Ann(M). Moreover, when Mˆ is equidimensional, ...
School on Commutative Algebra and Algebraic Geometry in Prime Characteristics, ICTP Trieste, May 2-5, 2023.
BCAM Severo Ochoa course "Introduction to multiplicity theory" Spring 2023.
RGAS School on Singularities, IMUS Sevilla, January 8-12, 2024.