more specifically in algebraic geometry, Parshin's conjecture (also referred to as the Beilinson–Parshin conjecture) states that for any smooth projective...

places. Aleksei Parshin showed that Shafarevich's finiteness conjecture would imply the Mordell conjecture, using what is now called Parshin's trick. Gerd...

the namesake of the terms "Parshin chain" and "Parshin's conjecture" Denis Parshin, Russian ice hockey player Georgy Parshin, Soviet World War II pilot...

generated by its contained derivations, then it must be smooth. Parshin's conjecture: the higher algebraic K-groups of any smooth projective variety defined...

as Parshin's trick, which gives an embedding of an algebraic curve into the Siegel modular variety. Shafarevich proved his finiteness conjecture for...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

conjecture of Iwasawa theory and in construction of higher regulators. Parshin's conjecture concerns the higher algebraic K-groups for smooth varieties over...

conjecture for K-groups of number rings, the Hodge conjecture, the Tate conjecture about algebraic cycles, the Birch and Swinnerton-Dyer conjecture about...

primes of bad reduction. The conjecture was proved by Gerd Faltings as a partial step in his proof of the Mordell conjecture. Shafarevich's students included...

Shimura varieties and a conjecture of Kottwitz", Inventiones mathematicae 194 (2013), No. 1, 147–254. "On the coherence conjecture of Pappas and Rapoport"...

studied by Gelfond and then solved by Alan Baker. It is called the Gelfond conjecture or Baker's theorem. Baker was awarded a Fields Medal in 1970 for this...

introducing Parshin's trick. In 1983 and 1984, Gerd Faltings completed the proof of the Mordell conjecture by proving the Shafarevich finiteness conjecture. The...

out to be of major importance in relation with the monstrous moonshine conjectures. The first several coefficients of the q-expansions of their Hauptmoduln...

investigators guessed that the stolen jewellery was hidden in a bag of flour. The conjecture was confirmed during the second search of Evseev's apartment. During the...

ideal when characteristic sets identify both ideals. The Kolchin catenary conjecture states given a d > 0 {\textstyle d>0} dimensional irreducible differential...

generalizations of trigonometric and elliptic functions. Through the Langlands conjectures, automorphic forms play an important role in modern number theory. In...

c_{1}:Pic(X)\to H^{2}(X,\mathbb {Z} )} . By Yau's solution of the Calabi conjecture, a smooth complex variety admits Kähler metrics of positive Ricci curvature...

complex manifolds, and the Grauert–Riemenschneider conjecture is a special case of the conjecture of Narasimhan. In fact it was the need to put (in particular)...