FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W3208484927> ?p ?o ?g. }

• W3208484927 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a smooth projective variety over an algebraically closed field, and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f colon upper X right-arrow upper X> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:<!-- : --></mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>fcolon Xto X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> a surjective self-morphism of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=i> <mml:semantics> <mml:mi>i</mml:mi> <mml:annotation encoding=application/x-tex>i</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-th cohomological dynamical degree <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=chi Subscript i Baseline left-parenthesis f right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>χ<!-- χ --></mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>chi _i(f)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is defined as the spectral radius of the pullback <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Superscript asterisk> <mml:semantics> <mml:msup> <mml:mi>f</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>f^{*}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on the étale cohomology group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Subscript ModifyingAbove normal e With acute normal t Superscript i Baseline left-parenthesis upper X comma bold upper Q Subscript script l Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mover> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>e</mml:mi> </mml:mrow> <mml:mo>´<!-- ´ --></mml:mo> </mml:mover> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>t</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>i</mml:mi> </mml:msubsup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>Q</mml:mi> </mml:mrow> <mml:mi>ℓ<!-- ℓ --></mml:mi> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H^i_{acute {mathrm {e}}mathrm {t}}(X, mathbf {Q}_ell )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-th numerical dynamical degree <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=lamda Subscript k Baseline left-parenthesis f right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>λ<!-- λ --></mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>lambda _k(f)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as the spectral radius of the pullback <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=f Superscript asterisk> <mml:semantics> <mml:msup> <mml:mi>f</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>f^{*}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on the vector space <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=sans-serif upper N Superscript k Baseline left-parenthesis upper X right-parenthesis Subscript bold upper R> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=sans-serif>N</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:msub> <mml:mo stretchy=false>)</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=bold>R</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:annotation encoding=application/x-tex>mathsf {N}^k(X)_{mathbf {R}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of real algebraic cycles of codimension <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=k> <mml:semantics> <mml:mi>k</mml:mi> <mml:annotation encoding=application/x-tex>k</mml:annotation> </mml:semantics> </mml:math> </inline-formula> on <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> modulo numerical equivalence. Truong conjectured that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=chi Subscript 2 k Baseline left-parenthesis f right-parenthesis equals lamda Subscript k Baseline left-parenthesis f right-parenthesis> <mml:semantics> <mml:mrow> <mml:msub> <mml:mi>χ<!-- χ --></mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mn>2</mml:mn> <mml:mi>k</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>λ<!-- λ --></mml:mi> <mml:mi>k</mml:mi> </mml:msub> <mml:mo stretchy=false>(</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>chi _{2k}(f) = lambda _k(f)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for all <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=0 less-than-or-equal-to k less-than-or-equal-to dimension upper X> <mml:semantics> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>k</mml:mi> <mml:mo>≤<!-- ≤ --></mml:mo> <mml:mi>dim</mml:mi> <mml:mo>⁡<!-- ⁡ --></mml:mo> <mml:mi>X</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>0 le k le dim X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> as a generalization of Weil’s Riemann hypothesis. We prove this conjecture in the case of abelian varieties. In the course of the proof we also obtain a new parity result on the eigenvalues of self-maps of abelian varieties in prime characteristic, which is of independent interest." @default.
• W3208484927 created "2021-11-08" @default.
• W3208484927 creator A5042274876 @default.
• W3208484927 date "2023-02-07" @default.
• W3208484927 modified "2023-09-30" @default.
• W3208484927 title "Eigenvalues and dynamical degrees of self-maps on abelian varieties" @default.
• W3208484927 cites W1589001499 @default.
• W3208484927 cites W1886898835 @default.
• W3208484927 cites W1979468839 @default.
• W3208484927 cites W1989130557 @default.
• W3208484927 cites W2012341045 @default.
• W3208484927 cites W2049920220 @default.
• W3208484927 cites W2074004788 @default.
• W3208484927 cites W2076178640 @default.
• W3208484927 cites W2087736116 @default.
• W3208484927 cites W2321143710 @default.
• W3208484927 cites W2331202706 @default.
• W3208484927 cites W2726751866 @default.
• W3208484927 cites W2952991934 @default.
• W3208484927 cites W2962857092 @default.
• W3208484927 cites W2963213673 @default.
• W3208484927 cites W2963224939 @default.
• W3208484927 cites W3007748585 @default.
• W3208484927 cites W3043485792 @default.
• W3208484927 cites W3101342511 @default.
• W3208484927 cites W3102752954 @default.
• W3208484927 cites W3106435937 @default.
• W3208484927 cites W3216994159 @default.
• W3208484927 cites W4230832653 @default.
• W3208484927 doi "https://doi.org/10.1090/jag/806" @default.
• W3208484927 hasPublicationYear "2023" @default.
• W3208484927 type Work @default.
• W3208484927 sameAs 3208484927 @default.
• W3208484927 citedByCount "2" @default.
• W3208484927 countsByYear W32084849272022 @default.
• W3208484927 countsByYear W32084849272023 @default.
• W3208484927 crossrefType "journal-article" @default.
• W3208484927 hasAuthorship W3208484927A5042274876 @default.
• W3208484927 hasBestOaLocation W32084849272 @default.
• W3208484927 hasConcept C11413529 @default.
• W3208484927 hasConcept C154945302 @default.
• W3208484927 hasConcept C2776321320 @default.
• W3208484927 hasConcept C33923547 @default.
• W3208484927 hasConcept C41008148 @default.
• W3208484927 hasConceptScore W3208484927C11413529 @default.
• W3208484927 hasConceptScore W3208484927C154945302 @default.
• W3208484927 hasConceptScore W3208484927C2776321320 @default.
• W3208484927 hasConceptScore W3208484927C33923547 @default.
• W3208484927 hasConceptScore W3208484927C41008148 @default.
• W3208484927 hasLocation W32084849271 @default.
• W3208484927 hasLocation W32084849272 @default.
• W3208484927 hasOpenAccess W3208484927 @default.
• W3208484927 hasPrimaryLocation W32084849271 @default.
• W3208484927 hasRelatedWork W1529400504 @default.
• W3208484927 hasRelatedWork W1892467659 @default.
• W3208484927 hasRelatedWork W2143954309 @default.
• W3208484927 hasRelatedWork W2333703843 @default.
• W3208484927 hasRelatedWork W2334690443 @default.
• W3208484927 hasRelatedWork W2386767533 @default.
• W3208484927 hasRelatedWork W2394022102 @default.
• W3208484927 hasRelatedWork W2469937864 @default.
• W3208484927 hasRelatedWork W2808586768 @default.
• W3208484927 hasRelatedWork W2998403542 @default.
• W3208484927 isParatext "false" @default.
• W3208484927 isRetracted "false" @default.
• W3208484927 magId "3208484927" @default.
• W3208484927 workType "article" @default.