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Motives over totally real fields and p -adic L -functions

Alexei A. Panchishkin (1994)

Annales de l'institut Fourier

Special values of certain L functions of the type L ( M , s ) are studied where M is a motive over a totally real field F with coefficients in another field T , and L ( M , s ) = ∏ 𝔭 L 𝔭 ( M , 𝒩 𝔭 - s ) is an Euler product 𝔭 running through maximal ideals of the maximal order 𝒪 F of F and L 𝔭 ( M , X ) - 1 = ( 1 - α ( 1 ) ( 𝔭 ) X ) · ( 1 - α ( 2 ) ( 𝔭 ) X ) · ... · ( 1 - α ( d ) ( 𝔭 ) X ) = 1 + A 1 ( 𝔭 ) X + ... + A d ( 𝔭 ) X d being a polynomial with coefficients in T . Using the Newton and the Hodge polygons of M one formulate a conjectural criterium for the existence of a p -adic analytic continuation of the special values. This conjecture is verified in a number of cases related to...

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension ≤ 4 and ≥ 11 . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real quadrics....

Motivic functors.

Dundas, Bjørn Ian, Röndigs, Oliver, Østvær, Paul Arne (2003)

Documenta Mathematica

Motivic-type invariants of blow-analytic equivalence

Satoshi Koike, Adam Parusiński (2003)

Annales de l'Institut Fourier

To a given analytic function germ f : ( ℝ d , 0 ) → ( ℝ , 0 ) , we associate zeta functions Z f , + , Z f , - ∈ ℤ [ [ T ] ] , defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies as well the blow-analytic...

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