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ZETA FUNCTIONS, GROTHENDIECK GROUPS, AND THE WITT RING
ZETA FUNCTIONS GROTHENDIECK GROUPS
2015/12/10
After preliminary definitions and a review (in the first section) of the basic structures (such as
Frobenius Fm and Verschiebung Vm) of the Witt ring W(R) of a ring R, we present our main...
Beginning with the conjecture of Artin and Tate in 1966, there has been a series of
successively more general conjectures expressing the special values of the zeta function
of an algebraic variety o...
The p-cohomology of algebraic varieties and special values of zeta functions
zeta functions algebraic varieties
2015/12/10
The p-cohomology of an algebraic variety in characteristic p lies naturally in the
category Db
c
.R/ of coherent complexes of graded modules over the Raynaud ring
(Ekedahl-Illusie-Raynaud). We stu...
For each ˉeld k, we deˉne a category of rationally decomposed mixed
motives with Z-coe±cients. When k is ˉnite, we show that the category is Tannakian, and we prove formulas relating the behaviour of...
We show that the coefficients in the Laurent series of the
Igusa local zeta functions I(s) = R
C
f
sω are periods. This is proved by
first showing the existence of functional equation...
Motivic zeta functions for degenerations of abelian varieties and Calabi-Yau varieties
Motivic zeta functions degenerations of abelian varieties Calabi-Yau varieties
2011/2/25
Let f ∈ Z[x1, . . . , xn] be a non-constant polynomial, and let p be a prime. Igusa’s p-adic zeta function Zp f (s) is a meromorphic function on the complex plane that encodes the number of solutions ...
Zeta functions and Bernstein-Sato polynomials for ideals in dimension two
Zeta functions Bernstein-Sato polynomials ideals dimension two
2011/2/28
For a nonzero ideal I ⊳C[x1, . . . , xn], with 0 ∈ supp I, a (general-ized) conjecture of Igusa–Denef–Loeser predicts that every pole of its topologi-cal zeta function is a root of its Bernstein...
On the zeros of Weng zeta functions for Chevalley groups
Weng zeta functions Chevalley groups
2010/11/23
We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over $\Q$ are simple and on the critical line.
Functional equations for Weng's zeta functions for $(G,P)/\mathbb{Q}$
Functional equations Weng's zeta functions
2010/11/23
It is shown that Weng's zeta functions associated with arbitrary semisimple algebraic groups defined over the rational number field and their maximal parabolic subgroups satisfy the functional equatio...
Milnor-Selberg zeta functions and zeta regularizations
Milnor-Selberg zeta functions zeta regularizations
2010/11/19
By a similar idea for constructing Milnor's gamma functions, we study ``higher depth determinants'' of the Laplacian on a compact Riemann surface of genus greater than one. We prove that, as a general...
Computing special values of partial zeta functions
Computing special values partial zeta functions
2010/10/29
We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the \emph{Eisenstein cocycle} $\Psi $, a group cocycle for $GL_{n} (\Z...