Related papers: A $p$-adic analogue of the Borel regulator and the…

Let $k$ be a totally real field, and let $A/k$ be an absolutely irreducible, polarized Abelian variety of odd, prime dimension whose endomorphisms are all defined over $k$. Then the only strictly compatible families of abstract, absolutely…

Our investigation focuses on an additive analogue of the Bloch-Gabber-Kato theorem which establishes a relation between the Milnor $K$-group of a field of positive characteristic and a Galois cohomology group of the field. Extending the…

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these…

We give proofs of de Rham comparison isomorphisms for rigid-analytic varieties, with coefficients and in families. This relies on the theory of perfectoid spaces. Another new ingredient is the pro-etale site, which makes all constructions…

Suppose that G is a connected reductive group over a p-adic field F, that K is a hyperspecial maximal compact subgroup of G(F), and that V is an irreducible representation of K over the algebraic closure of the residue field of F. We…

We show that the poset of alternating sign matrices, with Bruhat order, is isomorphic to the poset of certain submodules of the dominant Verma module for the special linear Lie algebra $\frak{sl}_n$. The latter poset consists of the…

We promote Lazard's Poincar\'e duality for p-adic Lie groups to spectrum coefficients. The key aspect is the determination of the dualizing object in terms of "linear" data, namely the adjoint representation.

We generalize Waldschmidt's bound for Leopoldt's defect and prove a similar bound for Gross's defect for an arbitrary extension of number fields. As an application, we prove new cases of Gross's finiteness conjecture (also known as the…

Let G be a finite group and p be a prime. We investigate isomorphism invariants of $\mathbb{Z}_{p}[G]$-lattices whose extension of scalars to $\mathbb{Q}_p$ is self-dual, called regulator constants. These were originally introduced by…

We present an algorithm to determine if the $L$-series associated to an automorphic representation and the one associated to an elliptic curve over an imaginary quadratic field agree. By the work of Harris-Soudry-Taylor, Taylor and…

As a natural sequel to the study of A-motivic cohomology initiated in "On the integral part of A-motivic cohomology", we develop a notion of regulator for rigid analytically trivial Anderson A-motives. In accordance with the conjectural…

We evaluate a rigid analytical analogue of the Beilinson-Bloch-Deligne regulator on certain explicit elements in the K_2 of Drinfeld modular curves, constructed from analogues of modular units, and relate its value to special values of…

Louveau and Rosendal [5] have shown that the relation of bi-embeddability for countable graphs as well as for many other natural classes of countable structures is complete under Borel reducibility for analytic equivalence relations. This…

We will formulate and prove a certain reciprocity law relating certain residues of the differential symbol dlog^2 from the K_2 of a Mumford curve to the rigid analytic regulator constructed by the author in a previous paper. We will use…

We investigate $p$-adic cohomologies of log rigid analytic varieties over a $p$-adic field. For a log rigid analytic variety $X$ defined over a discretely valued field, we compute the Kummer pro-\'etale cohomology of…

We improve the known results about the complexity of the relation of isomorphism between separable Banach spaces up to Borel reducibility, and we achieve this using the classical spaces $c_0$, $\ell_p$ and $L_p$, $1 \leq p <2$. More…

To the symmetric space of the (positive half) of a real loop group, we attach a Borel--Serre type bordification and equip it with a Hausdorff topology. The attached boundary, indexed by certain rational parabolics of the loop group, is…

We will prove that Ruelle L-function for a cuspidal local system on an odd dimensional hyperbolic manifold with finite volume satisfies a functional equation and an analog of the Riemann hypothesis. We will also compute its Laurent…

There are two infinitesimal (i.e., additive) versions of the $K$-theory of a field $F$: one was introduced by Cathelineau, which is an $F$-module, and another one introduced by Bloch-Esnault, which is an $F^*$-module. Both versions are…

We consider questions in Galois cohomology which arise by considering mod $p$ Galois representations arising from automorphic forms. We consider a Galois cohomological analog for the standard heuristics about the distribution of Wieferich…