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17 May 2024: On the average number of 2-Selmer elements of elliptic curves over F. ... Elliptic curves over Q. are modular. J. Eur. Math. Soc. 21 (2019), no.

11 Jan 2024: 3. Let X be a Poisson random variable of parameter λ (0, ). (a) By optimizing the estimate of Question 2(b) over β, show that, for all x λ,. ... yet appeared? (b) What is the probability that the entire culture dies out eventually?

28 Jan 2024: We fix T B Ga maximal torus and Borel pair in G defined over F which are in good positionrelative to s, and let I = Gal(F/F). ... We let B Tbe the Borel subgroup defined over F determined by BH and let X(T).

22 Jan 2024: Our main result computes these local probabilities for quadratic forms over thep-adics. ... Then Q is k-isotropic (and regular) over Qp. 4. 3 GLOBAL DENSITIES.

16 Jan 2024: has fibre V , and thus ρ(P) is a vector bundle over M. ... Let the Roman indices a, b, c,. run over the set {1,. ,

31 Jan 2024: 533.2 Direct sums and free modules. 573.3 Matrices over Euclidean domains. ... r (0R 0R) = r 0R. We now use the fact that multiplication distributes over addition.

29 May 2024: 2. R is a vector space over the field Q. A basis of R over Q is called a Hamelbasis. ... If B 6= A, thenfor any x A B, the extension (B,R) =. (B {x},R {(b,x) : b B}. )contradicts the maximality of (B,R).

11 Jan 2024: The set of (isomorphism classes of) irreducible smooth GL2(Ql)-modules(over C). • ... of potentialautomorphy [Tay02], together with an ‘R = T’ theorem over a suitable base exten-sion.

5 Jun 2024: functor F : J O(1)0 TopO(1) enriched over Top, where J. ... First let ξ and π be vector bundles over spaces B and B′, respectively, and fixsome bundle map I : ξ π.