Bertini theorems revisited

Ghosh, Mainak; Krishna, Amalendu

doi:10.1112/jlms.12778

Cited by 5 publications

(1 citation statement)

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“…We fix an embedding X ⊂ P N k and apply [20,Theorem 6.3] to find a hypersurface H ⊂ P N k such that the scheme-theoretic intersection Y = X ∩ H is normal and smooth along X o hypothesis from the famous Roitman torsion theorem [63]. Geisser [18] subsequently showed that the prime-to-p condition in the torsion theorem of Spieß and Szamuely could be eliminated if one assumed resolution of singularities.…”

Section: Relation With the Levine-weibel Chow Groupmentioning

confidence: 99%

Zero-Cycles on Normal Projective Varieties

Ghosh¹,

Krishna

2022

J. Inst. Math. Jussieu

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We prove an extension of the Kato–Saito unramified class field theory for smooth projective schemes over a finite field to a class of normal projective schemes. As an application, we obtain Bloch’s formula for the Chow groups of $0$ -cycles on such schemes. We identify the Chow group of $0$ -cycles on a normal projective scheme over an algebraically closed field to the Suslin homology of its regular locus. Our final result is a Roitman torsion theorem for smooth quasiprojective schemes over algebraically closed fields. This completes the missing p-part in the torsion theorem of Spieß and Szamuely.

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Section: Relation With the Levine-weibel Chow Groupmentioning

confidence: 99%

Zero-Cycles on Normal Projective Varieties

Ghosh¹,

Krishna

2022

J. Inst. Math. Jussieu

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The Noether–Lefschetz theorem in arbitrary characteristic

2024

J. Algebraic Geom.

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We show that if X ⊂ P k N X\subset \mathbb P^N_k is a normal variety of dimension ≥ 3 \geq 3 and H ⊂ P k N H\subset \mathbb P^N_k a very general hypersurface of degree d = 4 d=4 or ≥ 6 \geq 6 , then the restriction map Cl ⁡ ( X ) → Cl ⁡ ( X ∩ H ) \operatorname {Cl}(X)\to \operatorname {Cl}(X\cap H) is an isomorphism up to torsion. If dim ⁡ X ≥ 4 \dim X\geq 4 , the result holds for d ≥ 2 d\geq 2 . The proof uses the relative Jacobian of a curve fibration, together with a specialization argument, and the result holds over fields of arbitrary characteristic.

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