36 citations · 133 across the 20 of their papers we have counts for
6 papers · 1 filter
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.…
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…
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…
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…
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…