Idele class groups with modulus

Gupta, Rahul; Krishna, Amalendu

doi:10.48550/arxiv.2101.04609

Cited by 3 publications

(15 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The existence of p ± * has the same proof as that of [1, Proposition 5.9]. If k is infinite, then the assertion that τ * X descends to the level of Chow groups, is a direct consequence of Proposition 4.2 and the projective bundle trick of [12,Lemma 8.3], combined with the following two remarks. The first is that the cited result is proven when X is regular, but its proof only uses that X has singularity in codimension ≥ 2.…”

Section: 4mentioning

confidence: 75%

“…It is a natural question to ask if π adiv 1 (U, D) and π ab 1 (U, D) agree. This is known to be the case either D red is a simple normal crossing divisor on U (see Lemma 6.1) or if X is regular (see [12,Theorem 1.4]). We let π adiv 1 (U, D) 0 be the kernel of the canonical map π adiv 1 (U, D) → π ab 1 (Spec (k)).…”

Section: Introductionmentioning

confidence: 99%

“…The group π ab 1 (U, D) 0 is similarly defined. If X is regular, it follows from the main results [19], [2], [11] and [12] that there are isomorphisms of finite groups…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A decomposition theorem for 0-cycles and applications

Gupta¹,

Krishna²,

Rathore³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We describe the abelian étale fundamental group with modulus in terms of 0-cycles on a class of smooth quasi-projective varieties over finite fields which may not admit smooth compactifications. Using a limit process, this yields a cycle-theoretic analogue of the K-theoretic reciprocity theorem of Kato-Saito for such varieties. The proof is based on a decomposition theorem for the cohomological Chow group of 0-cycles on the double of a quasi-projective R 1 -scheme over a field along a closed subscheme in terms of the Chow groups with and without modulus of the scheme. This also extends the decomposition theorem of Binda-Krishna to smooth schemes over imperfect fields. Contents 1. Introduction 1 2. Levine-Weibel Chow group with modulus 6 3. Cartier curves on the double 11 4. The pull-back map τ * X 15 5. The exact sequence and applications 21 6. Reciprocity theorem for surfaces 26 7. Reciprocity theorem in higher dimensions 31 References 35

show abstract

Section: 4mentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A decomposition theorem for 0-cycles and applications

Gupta¹,

Krishna²,

Rathore³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Combining (1.4) with the main results of [8], [32] and [23,Thm. 1.4], we obtain the following reciprocity theorem for Russell's relative Chow group.…”

Section: Introductionmentioning

confidence: 71%

“…for a finite extension k ′ i whose degree is a power of ℓ i for each i = 1, 2. Using the projection formula for Chow groups with modulus (see [23,Prop. 8.5]), we conclude that ℓ n 1 1 α = ℓ n 2 2 α = 0 in CH 0 (X D) for some n 1 , n 2 ≥ 1.…”

Section: 3mentioning

confidence: 99%

Suslin homology via cycles with modulus and applications

Binda¹,

Krishna²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We show that for a smooth projective variety X over a field k and a reduced effective Cartier divisor D ⊂ X, the Chow group of 0-cycles with modulus CH 0 (X D) coincides with the Suslin homology H S 0 (X ∖ D) under some necessary conditions on k and D. Several consequences are derived. Contents 1. Introduction 1 2. Algebraic and homotopy K-groups of a double 6 3. Proof of the main result 13 4. Motivic cohomology of normal crossing schemes 19 5. Question of Barbieri-Viale and Kahn 24 References 25

show abstract

Ramified class field theory and duality over finite fields

Gupta¹,

Krishna²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

We prove a duality theorem for the p-adic étale motivic cohomology of a variety U which is the complement of a divisor on a smooth projective variety over F p . This extends the duality theorems of Milne and Jannsen-Saito-Zhao. The duality introduces a filtration on H 1 ét (U, Q Z). We identify this filtration to the classically known Matsuda filtration when the reduced part of the divisor is smooth. We prove a reciprocity theorem for the idele class groups with modulus introduced by Kerz-Zhao and Rülling-Saito. As an application, we derive the failure of Nisnevich descent for Chow groups with modulus.

show abstract

Idele class groups with modulus

Cited by 3 publications

References 24 publications

A decomposition theorem for 0-cycles and applications

A decomposition theorem for 0-cycles and applications

Suslin homology via cycles with modulus and applications

Ramified class field theory and duality over finite fields

Contact Info

Product

Resources

About