Logarithmic Hodge–Witt sheaves on normal crossing varieties

Sato, Kanetomo

doi:10.1007/s00209-006-0033-z

Cited by 22 publications

(43 citation statements)

References 27 publications

(41 reference statements)

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“…[Sat3], Theorem 2.7): ). By (1.2.2), it turns out that the sheaf H n (T r (n) X ) is generated by ι * (U 1 M n r ) and the image of (G m , X ) ⊗n , so that the image of the natural cup-product map [Sat2]. Moreover, we have the following isomorphism for n 1:…”

Section: Notationmentioning

confidence: 95%

“…where µ denotes the group of pth roots of unity in Frac(A); we need to consider several t's to prove Theorem 2.2 for a single n. The non-degeneracy of (2.2.1) is due to Milne [Mi1] in case Y is smooth, and proved by the author [Sat2] in case Y has normal crossings. The most delicate part of our duality is the non-degeneracy of (2.2.2).…”

Section: Arithmetic Duality Theoremsmentioning

confidence: 99%

“…In this paper, we like to survey recent results of the author [Sat2], [Sat3] and his joint work with Shuji Saito [SaSa] (cf. [JSS]).…”

Section: Introductionmentioning

confidence: 99%

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Higher-dimensional arithmetic using <i>p</i>-adic étale Tate twists

Sato

2005

Homology, Homotopy and Applications

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This paper is a survey on recent researches of the author and his recent joint work with Shuji Saito. We will explain how to construct p-adicétale Tate twists on regular arithmetic schemes with semistable reduction, and state some fundamental properties of those objects. We will also explain how to define cycle class maps from Chow groups toétale cohomology groups with coefficients in p-adicétale Tate twists and state injectivity and surjectivity results on those new cycle class maps. Dedicated to V. Snaith on his 60th birthday

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Section: Notationmentioning

confidence: 95%

Section: Arithmetic Duality Theoremsmentioning

confidence: 99%

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Higher-dimensional arithmetic using <i>p</i>-adic étale Tate twists

Sato

2005

Homology, Homotopy and Applications

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“…. Secondly, by [33], ν n−1 Z,r on normal crossing variety admits Gersten resolution. By Lemma 4.6, higher Chow groups on normal crossing varieties admits Gersten resolution as well.…”

Section: 3))mentioning

confidence: 97%

Comparison of dualizing complexes

Zhong

2013

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We prove that there is a map from Bloch's cycle complex to Kato's complex of Milnor K-theory, which induces a quasi-isomorphism from cycle complex mod p r to Moser's complex of logarithmic de Rham-Witt sheaves. Next we show that the truncation of Bloch's cycle complex at −3 is quasi-isomorphic to Spiess' dualizing complex. In the end, we prove that a weak form of the Gersten Conjecture implies that Sato's dualizing complex is quasi-isomorphic to Bloch's complex.

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“…If X is smooth then both ν n X,r and λ n X,r agree with the sheaf W r Ω n X,log . We next review the duality result in [Sat1]. For integers m, n ≥ 0, there is a natural pairing of sheaves…”

Section: Notation and Conventions (I)mentioning

confidence: 99%

Duality for p-adic étale Tate Twists with modulus

Yamamoto¹

2022

Preprint

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In this paper, we define p-adic étale Tate twists for a modulus pair (X, D), where X is a regular semi-stable family and D is an effective Cartier divisor on X which is flat over a base scheme. The main result of this paper is an arithmetic duality of p-adic étale Tate twists for proper modulus pairs (X, D), which holds as a pro-system with respect to the multiplicities of the irreducible components of D. m 21 5.1. Setting 22 5.2. Construction of Θ r D 22 5.3. Explicit formula for Θ r D 23 5.4. Proof of (⊛2) 28 6. Duality for M r m 28 6.1. Proof of Theorem 6.1 30 7. Proof of Theorem 1.1 33 8. Proof of non-degeneracy of the pairing in Theorem 1.1 37 8.1. Descending induction on r 37 8.2. Proof of Proposition 39 9. Acknowledgements 42 References 42

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Logarithmic Hodge–Witt sheaves on normal crossing varieties

Abstract: In this paper, we define two kinds (homological and cohomological) of étale logarithmic Hodge-Witt sheaves on normal crossing varieties over a perfect field of positive characteristic, and discuss some fundamental properties, in particular puity and duality.

Cited by 22 publications

References 27 publications

Higher-dimensional arithmetic using <i>p</i>-adic étale Tate twists

Higher-dimensional arithmetic using <i>p</i>-adic étale Tate twists

Comparison of dualizing complexes

Duality for p-adic étale Tate Twists with modulus

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