36 citations · 133 across the 20 of their papers we have counts for
20 papers
Derived categories of curves of genus one and torsors over abelian varieties
Niranjan Ramachandran, Jonathan Rosenberg
Suppose is a smooth projective curve of genus 1 over a perfect field , and is its Jacobian. In the case that has no -rational points, so that and are not…
Values of zeta functions of arithmetic surfaces at
S. Lichtenbaum, N. Ramachandran
We show that the recent conjecture of the first-named author for the special value at of the zeta function of an arithmetic surface is equivalent to the Birch-Swinnerton-Dyer…
Fiber integration of gerbes and Deligne line bundles
Ettore Aldrovandi, Niranjan Ramachandran
Let be a family of smooth projective curves, and let and be a pair of line bundles on . We show that Deligne's line bundle can be obta…
Cup products, the Heisenberg group, and codimension two algebraic cycles
Ettore Aldrovandi, Niranjan Ramachandran
We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper alg…
Higher Euler characteristics
Niranjan Ramachandran
We provide a natural interpretation of the secondary Euler characteristic and introduce higher Euler characteristics. For a compact oriented manifold of odd dimension, the secondar…
A note on the Bloch-Tamagawa space and Selmer groups
Niranjan Ramachandran
For any abelian variety over a number field, we construct an extension of the Tate-Shafarevich group by the Bloch-Tamagawa space using the recent work of Lichtenbaum and Flach.…
Exponentiation of motivic measures
Niranjan Ramachandran, Goncalo Tabuada
In this short note we establish some properties of all those motivic measures which can be exponentiated. As a first application, we show that the rationality of Kapranov's zeta fu…
Zeta functions, Grothendieck groups, and the Witt ring
Niranjan Ramachandran
We prove some results connecting the zeta functions of varieties over finite fields with the big Witt ring over . We explore relations with motivic measures and a classi…
Motivic complexes and special values of zeta functions
James Milne, Niranjan Ramachandran
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 a…
The p-cohomology of algebraic varieties and special values of zeta functions
James S. Milne, Niranjan Ramachandran
The p-cohomology of an algebraic variety in characteristic p lies naturally in the category of coherent complexes of graded modules over the Raynaud ring (Ekedahl-Il…
Motivic complexes over finite fields and the ring of correspondences at the generic point
James S. Milne, Niranjan Ramachandran
Already in the 1960s Grothendieck understood that one could obtain an almost entirely satisfactory theory of motives over a finite field when one assumes the full Tate conjecture.…
Values of zeta functions at s=1/2
Niranjan Ramachandran
We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the sp…
KMS states and complex multiplication
Alain Connes, Matilde Marcolli, Niranjan Ramachandran
We construct a quantum statistical mechanical system which generalizes the Bost-Connes system to imaginary quadratic fields K of arbitrary class number and fully incorporates the e…
The de Rham-Witt and Z_p-cohomologies of an algebraic variety
James S. Milne, Niranjan Ramachandran
We show how the Z_p(r)-cohomologies of a smooth projective algebraic variety can be obtained via its de Rham-Witt complex.
Extensions of abelian varieties defined over a number field
Matthew A. Papanikolas, Niranjan Ramachandran
We study the arithmetic aspects of the finite group of extensions of abelian varieties defined over a number field. In particular, we establish relations with special values of L-f…
Integral Motives and Special Values of Zeta Functions
James S. Milne, Niranjan Ramachandran
For each field k, we define an abelian category of rationally decomposed mixed motives with integer coefficients. When k is finite, we show that the category is Tannakian, and we p…
A Weil-Barsotti formula for Drinfeld modules
Matthew A. Papanikolas, Niranjan Ramachandran
We study the group of extensions in the category of Drinfeld modules and Anderson's t-modules, and we show in certain cases that this group can itself be given the structure of a t…
From Jacobians to one-motives: exposition of a conjecture of Deligne
Niranjan Ramachandran
Deligne has conjectured that certain mixed Hodge theoretic invariants of complex algebraic invariants are motivic. This conjecture specializes to an algebraic construction of the J…
One-motives and a conjecture of Deligne
Niranjan Ramachandran
We introduce new motivic invariants of arbitrary varieties over a perfect field. These cohomological invariants take values in the category of one-motives (considered up to isogeny…
Duality of Albanese and Picard 1-motives
Niranjan Ramachandran
We define Albanese and Picard 1-motives of smooth (simplicial) schemes over a perfect field. For smooth proper schemes, these are the classical Albanese and Picard varieties. For a…