2004
DOI: 10.1007/s10240-004-0026-6
|View full text |Cite
|
Sign up to set email alerts
|

On the conductor formula of Bloch

Abstract: In [6], S. Bloch conjectures a formula for the Artin conductor of the -adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

0
91
0

Year Published

2005
2005
2021
2021

Publication Types

Select...
6
1

Relationship

1
6

Authors

Journals

citations
Cited by 71 publications
(91 citation statements)
references
References 31 publications
0
91
0
Order By: Relevance
“…Secondly, we are hopeful that the development of a theory of log cotangent complexes can be useful in the study of intersection theory on degenerations of varieties. In fact, the beginnings of a theory of log cotangent complexes can be found in the recent work of K. Kato and T. Saito ( [12]) on logarithmic localized intersection product, where it is used to study a proper scheme over a complete discrete valuation ring whose reduced closed fiber is a divisor with normal crossings.…”
Section: Introductionmentioning
confidence: 99%
“…Secondly, we are hopeful that the development of a theory of log cotangent complexes can be useful in the study of intersection theory on degenerations of varieties. In fact, the beginnings of a theory of log cotangent complexes can be found in the recent work of K. Kato and T. Saito ( [12]) on logarithmic localized intersection product, where it is used to study a proper scheme over a complete discrete valuation ring whose reduced closed fiber is a divisor with normal crossings.…”
Section: Introductionmentioning
confidence: 99%
“…As X is regular, this group is naturally identified with the Grothendieck group G(Y ) of coherent sheaves of Y , with Kato-Saito's notation in [KS1]. As X /S is proper, we have a degree homomorphism (Euler-Poincaré characteristic)…”
Section: The Case Of Local Fields: Swan Conductorsmentioning
confidence: 99%
“…For an explicit local description, see Example 2.2 in Section 2.2. For more intrinsic definition in the language of log geometry, we refer to [30,Section 4]. We introduce the log product in order to focus on the wild ramification.…”
Section: Euler Numbersmentioning
confidence: 99%
“…For the generality on log schemes, we refer to [26] and [30,Section 4]. In the classical case where the residue field is perfect, the two filtrations are the same up to the shift by 1.…”
Section: For a Subfield M ⊂ L Galois Over K And For A Rational Numbermentioning
confidence: 99%