17 citations · 30 across the 12 of their papers we have counts for
13 papers
Equi-dimensionalization via subdivision of simplices
Wataru Kai
We give an alternative proof of Suslin's equi-dimensionalization moving lemma using a different geometric construction. The new construction provides better control of the degrees…
Linear patterns of prime elements in number fields
Wataru Kai
We prove a number field analogue of the Green--Tao--Ziegler theorem on simultaneous prime values of degree 1 polynomials whose linear parts are pairwise linearly independent. Appli…
Notes on Mitsui's Prime Number Theorem with Siegel zeros
Wataru Kai
In these notes, we refine Mitsui's Prime Number Theorem from 1957, which for a number field predicts the number of prime elements in a bounded convex set in $K \otimes _{\mathb…
Unramified logarithmic Hodge-Witt cohomology and -invariance
Wataru Kai, Shusuke Otabe, Takao Yamazaki
Let be a smooth proper variety over a field and suppose that the degree map is isomorphic for any field extension . We sh…
The Green-Tao theorem for affine curves over F_q
Wataru Kai
Green and Tao famously proved in a 2008 paper that there are arithmetic progressions of prime numbers of arbitrary lengths. Soon after, analogous statements were proved by Tao for…
Constellations in prime elements of number fields
Wataru Kai, Masato Mimura, Akihiro Munemasa +2
Given any number field, we prove that there exist arbitrarily shaped constellations consisting of pairwise non-associate prime elements of the ring of integers. This result extends…
Isomorphisms up to bounded torsion between relative -groups and Chow groups with modulus
Ryomei Iwasa, Wataru Kai
In this note, we establish isomorphisms up to bounded torsion between relative -groups and Chow groups with modulus as defined by Binda-Saito.
Chern classes with modulus
Ryomei Iwasa, Wataru Kai
In this paper, we construct Chern classes from the relative -theory of modulus pairs to the relative motivic cohomology defined by Binda-Saito. An application to relative motivi…
Suslin's moving lemma with modulus
Wataru Kai, Hiroyasu Miyazaki
The moving lemma of Suslin states that a cycle on meeting all faces properly can be moved so that it becomes equidimensional over . This leads…
A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map
Wataru Kai
We present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties over -adic fields in terms of the Néron-Severi gro…
A moving lemma for algebraic cycles with modulus and contravariance
Wataru Kai
We prove a moving lemma which implies the contravariance of Bloch-Esnault's additive higher Chow group in smooth affine varieties and Binda-Saito's higher Chow group (taken in the…
Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus
Federico Binda, Jin Cao, Wataru Kai +1
The notion of modulus is a striking feature of Rosenlicht-Serre's theory of generalized Jacobian varieties of curves. It was carried over to algebraic cycles on general varieties b…
Notes on a p-adic exponential map for the Picard group
Wataru Kai
Part of these notes was written as the author's 2013 master thesis. For proper flat schemes over a complete discrete valuation ring of mixed characteristic, we construct an isomorp…