Birational localization of motivic spaces over perfect fields is equivalent to S^{2,1}-nullification, making π0^{b A^1} a birational invariant for proper schemes.
C., Garg, R., Singh, J
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The variety of skew braces is not action accessible.
Cochordal zero-divisor graphs of chain rings admit refined Betti formulas yielding 2-linear resolutions for the studied quotient rings.
Upper bounds on the number of irreducible factors of certain integer polynomials are obtained from prime factorizations of evaluated values and complex root locations, extending to bivariate polynomials via non-Archimedean valuations.
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Birational Algebraic Topology
Birational localization of motivic spaces over perfect fields is equivalent to S^{2,1}-nullification, making π0^{b A^1} a birational invariant for proper schemes.
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Action accessibility in the variety of skew braces
The variety of skew braces is not action accessible.
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Betti numbers for cochordal zero-divisor graphs of commutative rings
Cochordal zero-divisor graphs of chain rings admit refined Betti formulas yielding 2-linear resolutions for the studied quotient rings.
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Prime numbers and factorization of polynomials
Upper bounds on the number of irreducible factors of certain integer polynomials are obtained from prime factorizations of evaluated values and complex root locations, extending to bivariate polynomials via non-Archimedean valuations.