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The Manin constant in the semistable case

- Kestutis Cesnavicius
- Mathematics
- Compositio Mathematica
- 8 March 2017

For an optimal modular parametrization $J_{0}(n){\twoheadrightarrow}E$ of an elliptic curve $E$ over $\mathbb{Q}$ of conductor $n$ , Manin conjectured the agreement of two natural $\mathbb{Z}$… Expand

8 4- PDF

Poitou-Tate without restrictions on the order

- Kestutis Cesnavicius
- Mathematics
- 9 October 2014

The Poitou-Tate sequence relates Galois cohomology with restricted ramification of a finite Galois module $M$ over a global field to that of the dual module under the assumption that $\#M$ is a unit… Expand

9 3- PDF

MODULARITY LIFTING THEOREMS-NOTES FOR ARIZONA WINTER SCHOOL-DRAFT VERSION

- T. Gee, Kevin Buzzard, +9 authors Sug Woo Shin
- 2013

5 2- PDF

Selmer groups as flat cohomology groups

- Kestutis Cesnavicius
- Mathematics
- 21 January 2013

Given a prime number $p$, Bloch and Kato showed how the $p^\infty$-Selmer group of an abelian variety $A$ over a number field $K$ is determined by the $p$-adic Tate module. In general, the… Expand

10 1- PDF

The $A_{\text{inf}}$ -cohomology in the semistable case

- Kestutis Cesnavicius, Teruhisa Koshikawa
- Mathematics
- Compositio Mathematica
- 17 October 2017

For a proper, smooth scheme $X$ over a $p$ -adic field $K$ , we show that any proper, flat, semistable ${\mathcal{O}}_{K}$ -model ${\mathcal{X}}$ of $X$ whose logarithmic de Rham cohomology is… Expand

16 1- PDF

The $p$-parity conjecture for elliptic curves with a $p$-isogeny

- Kestutis Cesnavicius
- Mathematics
- 2 July 2012

For an elliptic curve $E$ over a number field $K$, one consequence of the Birch and Swinnerton-Dyer conjecture is the parity conjecture: the global root number matches the parity of the Mordell-Weil… Expand

3 1- PDF

TOPOLOGY ON COHOMOLOGY OF LOCAL FIELDS

- Kestutis Cesnavicius
- Mathematics
- Forum of Mathematics, Sigma
- 8 May 2014

Arithmetic duality theorems over a local field $k$ are delicate to prove if $\text{char}\,k>0$. In this case, the proofs often exploit topologies carried by the cohomology groups $H^{n}(k,G)$ for… Expand

11- PDF

The ℓ-parity conjecture over the constant quadratic extension

- Kestutis Cesnavicius
- Mathematics
- Mathematical Proceedings of the Cambridge…
- 12 February 2014

Abstract For a prime ℓ and an abelian variety A over a global field K, the ℓ-parity conjecture predicts that, in accordance with the ideas of Birch and Swinnerton–Dyer, the ℤℓ-corank of the ℓ∞-Selmer… Expand

8- PDF

Selmer groups and class groups

- Kestutis Cesnavicius
- Mathematics
- Compositio Mathematica
- 16 July 2013

Abstract Let $A$ be an abelian variety over a global field $K$ of characteristic $p\geqslant 0$. If $A$ has nontrivial (respectively full) $K$-rational $l$-torsion for a prime $l\neq p$, we exploit… Expand

8- PDF

Local factors valued in normal domains

- Kestutis Cesnavicius
- Mathematics
- 12 December 2013

We give an exposition of Deligne’s theory of local ϵ0-factors over fields and discrete valuation rings under the assumption that the theory over the complex numbers is known. We then employ standard… Expand

5- PDF

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